There's no change as far as I understand it.
ScalaTest made this change in 3.1.0 because they wanted to re-use the FlatSpec (FunSpec, etc.) names for new testing methods that would return assertions. I'm not 100% sure on all the changes, but AnyFlatSpec is an exact replacement for the old FlatSpec where the return type is Any.
There's some more info in the release notes for 3.1.0 (including multiple tables that show the old and new names) as well as Scalafix stuff they provide that may do the renames/upgrade for you:
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https://www.scalatest.org/release_notes/3.1.0
Sorry about that. Naming is apparently hard for other projects, too. :)