This is a necessarily incomplete answer, but gathers together a lot of the relevant data points.
There are basically two parts of this question.
One must both estimate the aggregate net worth of the cabinet, each time its membership changed, and one must estimate the share of wealth of less affluent Americans.
The Changing Definition of the Cabinet
One confounding factor regarding the first estimate is that the cabinet has grown larger over time. In 1789, there were just five heads of cabinet departments: the Secretary of State, the Secretary of Treasury, the Secretary of War, the Attorney General, and the Postmaster General.
There are now fifteen cabinet departments. Also every (or almost every) President has had some additional senior presidential advisors and independent agency heads have been included in the cabinet.
Today (per the 2016 World Almanac) these include the Vice President, the White House Chief of Staff, the head of the EPA, the director of the Office of Management and Budget, the U.S. Trade Representatives, the ambassador to the U.N., the chair of the Council of Economic advisors and the administrator of the Small Business administration, for a total of 23 people in addition to the President in the cabinet.
Most Presidents have more than one person serving in any particular cabinet post during their term of office, and there is a fair amount of turnover. For example, there have been 67 people who have served as Secretary of State since 1789 over the course of 44 Presidential administrations.
It is also worth recalling that until the Civil War, the federal government was a profoundly smaller institution. There was much higher turnover even in top positions like members of Congress and judges in the federal courts, because prior to the Civil War, a much larger share of government activity took place at the state and local level and the primary source of federal government revenue was customs duties.
Thus, in the early part of the Republic, cabinet posts lacked the prestige that they have today. Today, that prestige makes it possible for someone like President Obama or President Trump to obtain the willing cooperation of cabinet nominees who are taking a huge pay cut to do their job in the cabinet. Earlier on, the salary was a much bigger share of the draw for these jobs because there wasn't nearly as much prestige involved. So it was harder to get the very rich to serve in those posts.
The Difficult Practical and Definitional Issues
To really get a solid answer you would need detailed biographical information on several hundred individuals, and would also need to convert their wealth at the time into inflation adjusted amounts. And, you do need detail and an ability to determine wealth while in cabinet (presumably the desired definition) when lots of available data can demonstrate peak wealth (often based upon probate information) but not wealth precisely while in the cabinet.
For example, Secretary of Treasury Alexander Hamilton (who created the U.S. Mint and the predecessor to the Coast Guard while in office), is remembered as rather patrician - he was the grandson of an aristocrat, married a daughter of an affluent man, was a lawyer, founded the Bank of New York, helped reestablish Columbia College, was a co-founder of a major manufacturing company, and founded the New York Evening Post. But, while he undoubtedly became a member of the upper class in one sense, he was a poor orphan as a child, he made most of his money from government salaries, did not have a particularly profitable law practice, saw the manufacturing company go bankrupt, and because he died young in a duel, didn't live long enough to see some of his investments in other enterprises come to fruition.
Thomas Jefferson was an early Secretary of State before he served as President. He had a peak net worth of $234 million in 2016 dollars (more than any other cabinet member who later went onto serve as President although George Washington net worth in current dollars was about $580 million and Donald Trump's is more as well; see also here). But, he died broke.
JFK would have had a net worth of close to $1 billion had he lived to inherit his share of his family's estate, but of course, he did not. I believe that RFK also never came into the bulk of the family wealth he was heir to during his lifetime.
Benjamin Franklin served in the cabinet as Postmaster General and had a peak wealth of about $10 billion in current dollars, making cabinets including him competitive with the wealthiest, although, at a time of much less wealth and income inequality. But, the fact that his term as postmaster was under the Confederacy, that predated the current federal constitution adopted in 1789, muddies the question of whether he even "counts" for purposes of the original post. Franklin is arguably the wealthiest individual ever to serve in a prominent role in the United States government, Trump included.
The combined net worth of the members of President Obama's cabinet is on the order of $3 billion including Hillary Clinton at $31 million and chief of staff Bill Daley at $29 million, and a billionaire commerce secretary. (Trump's cabinet nominees have a combined net worth on the order of $15 billion plus which multiple historians have stated is the wealthiest ever).
Generally, the wealth of the top two or three most wealthy cabinet members will dwarf the wealth of everyone else in the cabinet combined, which somewhat eases the biographical challenge. Historically, the most wealthy members of the cabinet have tended to be Treasury Secretaries or Commerce Secretaries (the Commerce and Labor Department was formed in 1903 and was split into two departments in 1913).
The Gilded Age of the late 19th century was another period with many very affluent individuals actively involved in politics.
Still, particularly in light of the pattern of Presidential wealth over the years, there seems to be little doubt that cabinet members over the years have had considerably less than the combined wealth of Trump's proposed cabinet.
A historic average is much harder to come up with.
One useful reference point is that while the American South absolutely had a wealthy plantation, slave owner class, this was an oligarchy and not a winner take all economy like modern big businesses which dominate a national market.
The largest plantation in the nation in 1860 had 1,131 slaves (and this was larger than the largest plantation in the nation in 1850). Only 19 families in the entire nation in 1860 (none of whom had a sitting cabinet member) had more than 500 slaves. Only a handful of plantations were in more than two or three counties and almost all were entirely within a single state. Not a single firm in the entire South had even 0.1% share of the entire cotton producing market in the American South.
George Washington's plantation had about 220 slaves at its peak and a few indentured servants, which suggests that the wealthiest plantation owners in the United States probably still never had a net worth much over $1 billion in current U.S. dollars (doubling Washington's peak estimated net worth). And, Washington would have been in the top 1% of plantation owners, and at least the top 0.3% of the general population in wealth, at the time.
The wealthiest bankers and heads of manufacturing enterprises in the North (which was home to 90% of U.S. manufacturing on the eve of the Civil War and a much larger percentage during Reconstruction) would have been wealthier than any plantation owner in the U.S. for almost all of its post-1789 history. A list of the wealthiest persons in U.S. history is informative.
There have always been very wealthy people in the U.S., but given the smaller scale of the largest enterprises in the U.S. then, relative to today, and the fact none of the very wealthiest of the Gilded Age figures ever held cabinet positions, today's richest people are significantly wealthier than those in most of our history in constants 2016 dollars.
Overall income and wealth inequality
While measuring wealth inequality is the ultimate goal, better data is available for income inequality (because much of it can be gleaned from centrally collected income tax data collected annually), however, and income inequality and wealth inequality are highly correlated, although wealth inequality is generally more extreme than income inequality.
A 2012 article in the Atlantic magazine supplies lots of useful information regarding the latter point, looking at data points in 1774, 1860 and 2010. Generally speaking, income inequality has risen in that time period. For example, the GINI coefficient (a standard measure of income inequality that ranges from 0 with perfect equality to 1 with perfect inequality, i.e. one person having all income) in the 13 colonies in 1774 was 0.437 (much lower than all industrializing countries in Europe at the time), 0.51 in 1860 (a peak in U.S. history), a pre-Great Recession peak slightly above 0.50 and a 2012 value of around 0.47. In 2015, the last year for which estimates are available, it was 0.482. Another source notes a post-Civil War, pre-WWII peak just before the Great Depression in around 1929 at about 0.50.
Generally speaking income and wealth inequality are higher after long periods of economic growth, and are lower at the bottom of the business cycle.
By comparison, the highest GINI index in the world is 63.2 (Lesotho), the highest out of Africa is 59.2 (Haiti), and the highest in Europe is 46.0 (Georgia).
The key point is that the U.S. is slightly below the peak of about 0.50-0.51 reached just before the Civil War, possibly in the Gilded Age (between the numerous panics), around 1929, and around 2007-2008.
This means that at any points in time other than those moments, the cabinet would have had to have been significantly wealthier to have the wealth of 1/3rd of U.S. households, because wealth inequality would have been lower, and that at those peaks, simply comparing the cabinet wealth then in current dollars to cabinet wealth now in current dollars would suffice.
