The FBI routinely monitors calls to the Russian Embassy. They sent a transcript of conversations between Mike Flynn and the Russian ambassador to the Justice Department. The White House was provided the transcript with a warning that it made Flynn a target for Russian blackmail. Flynn remained on the job and Kellyanne Conway told a TV interviewer that Trump had complete confidence in Flynn the day before he resigned. What caused the White House to force Flynn to resign?
One explanation for Flynn's resignation is that the FBI transcript was leaked to the press. Trump tweeted about the leak and warned that he was taking actions to prevent future leaks. The fact, that the press had copies of the leaked transcript made it impossible for Trump to keep him in his job. The next question that remains to be answered is any relationship between Flynn's discussion of US sanctions relief in return for Russian assistance in the presidential election. That investigation should be going forward. The danger to Trump is that Flynn would not have made the call without Trump's knowledge and approval.
By the way, there are video links in this article showing Kellyanne Conway's efforts to spin the information during TV interviews. She has an almost impossible job defending Trump and his administration. She looks like she has aged several years since she took the job.