The FCC, like other federal agencies, is independent. There's nothing in the article to suggest that Carr's decision to do this has anything to do with Trump, who doesn't actually have authority here. Per the article, Carr apparently doesn't think he did anything coercive either. He's just making public statements. The supposed "threat" doesn't seem to me like much of one.

And Carr is also irrelevant to the Kimmel firing. ABC faced pressure from affiliates and his ratings had been declining for a long time.