It's a bit hard to research non-presidential elections that old online, but from what I've seen, his platform appears to have consisted mostly of "I'm better than my opponents." He was also for lower taxes, cutting government spending, removing political corruption, as well as prohibiting other "sin"-type things (such as alcohol). But every reference I can find has discussed his campaigns in terms of the attack ads, especially the "unusually personal terms" that his campaign advertising used.
Some examples (all emphasis mine):
Southern Poverty Law Center:
Phelps, undertaking a run for governor of Kansas, begins disseminating flyers attacking his gubernatorial competitors and other state politicians in unusually personal terms. He loses the Democratic primary, but garners 11,634 votes, 6.7% of the total.
Running for the U.S. Senate, Phelps gets a remarkable 30.8% of the ballots cast in the Democratic primary even as he terms his opponent a "bull dike" [sic].
"TV political ads – make or break" from the Topeka Capital Journal:
The Washburn researchers uncovered other examples of hard-charging political advertising:
• 1990 Democratic primary candidate Fred Phelps against Carlin, "John Carlin is the Michael Dukakis of Kansas."
The Kansas Historical Society's interview with former Governor Carlin:
The third candidate in the 1990 Democratic gubernatorial primary was Baptist minister Fred Phelps, who emphasized Carlin’s responsibility for the repeal of Kansas liquor-by-the-drink laws. He was not yet in the national spotlight because of his church’s pickets of the funerals of homosexuals and U. S. servicemen and women.
Then, from Carlin's own words:
To put this in context, in 1988 the Phelps family was very, very
active, and publicly so, in the Al Gore [presidential] campaign. It was before going crazy on the gay stuff. “Before the Now Fred Phelps,” is the way to put it. We had endless primary
debates. Debating Joan Finney and Fred Phelps was like a nightmare. I
mean, it was a nightmare. The classic one with Fred was at a
Hutchinson church. And see, what I had failed to acknowledge, both of
them were attacking me. Joan Finney attacked me because I was not a
populist. I was opposed to initiative and referendum. I was opposed to
the people running the state of Kansas, okay?
Anyway this night at this church, they’re both going after me, but Fred Phelps’s attack is: “John, I love you like a brother but, you know, on liquor by the drink, you’re wrong.” He
didn’t get into the gay issue; they were starting that a little bit, but he didn’t bring that out in the campaign, but he did the alcohol issue. He said, “Every death on the highways in Kansas, it’s your fault, John Carlin, and the people of
Kansas need to remember that. He’s the one that has brought us all
these alcohol problems. We wouldn’t have this if he didn’t do it.”
But anyway, Fred Phelps that night at the Hutchinson church says,
“John, I love you like a brother but you’re just as dumb as molasses
on this one.” Just ripped me, but it was over and over, the standard:
“John I love you like a brother, but . . . .” So at the end of the
debate, I had the end of my ninety seconds to wrap up and so I turned
to Fred and said, “Fred you know we have a lot of these to go,” (this
is maybe June), “we have a lot of these to go. If you keep up this
‘You know, I love you like a brother,’ by the time we get to the
election, people are going to start to get suspicious about our
relationship.” He went white as a sheet and had no response. That was
one of my great moments with Fred Phelps. He’s gone from that position
he took then to what I think is literally hating me. I don’t know if
I’d put it in the context of hate or not but it comes out like that
when they attack people.
The most descriptive article I was able to find was a 1990 article from the Laurence Journal-World, which interspersed attacks on the other candidates with actual platform positions:
An ordained Baptist minister who has been pastor at Westboro Baptist Church in Topeka since 1955, Phelps is running, or riding, a grass roots campaign. He strongly attacked other candidates who say they need piles of money to run for office, especially Gov. Mike Hayden.
"HAYDEN SAYS he needs $2 million to make the race; that's obscene," Phelps said. "Only a witch doctor needs to package himself in slick televison ads to cast an image."
Phelps said increased property taxes brought about by reappraisal and classification is the top issue in the campaign.
Phelps said his solution is to do away with property taxes entirely. He said the only taxes needed "if government is debloated, and the fat cut out" are the present levels of income and sales taxes.
Phelps called Carlin and Hayden the "tax twins" but had no comment about Finney.
THE OTHER most important issue, Phelps said, is "sleaze in government."
He called for the enactment of a tough code of ethics for public officials, spending limits for public officials' salaries and required public votes on pay increases, prohibiting the hiring of outside lawyers to do state legal work and banning lobbyist and lobbying activities.