In 1971, Senator Mike Gravel famously used his Congressional free speech privileges to publish a classified report on US activities in Vietnam, later dubbed "the Pentagon Papers". Did any members of Congress use their privileges in the same manner since then?
The precise parameters of the question are somewhat unclear in terms of what would constitute use of "their free speech privileges". Mike Gravel received leaked, classified documents which he had entered into the Congressional record, and then later also published by the private publishing company Beacon Press. Federal courts decided that this was not constitutionally protected speech. The case, Gravel v. United States eventually made it to the Supreme Court and the decision of the lower courts was overturned. In other words, the Supreme Court ruled 5-4 that publishing the Papers by a Congressional aid was, under these specific circumstances, protected speech.
If the question is whether a Congressperson has ever used the legal precedent of Gravel v. the United States in their own defense, I'm not aware of any such case.
However, a somewhat different situation of recent interest was the release of a classified memo on government surveillance by Rep. Devin Nunes in early 2018. As Molly Reynolds explains in a Lawfare blog post, this release was permissible based on an obscure clause in the Standing Rules that govern congressional committees, which allows for such releases when it is in the "public interest".