You are misinformed.
Go read the guilty plea.
That’s what Flynn or being sentenced for. There is no mention of Logan Act.
He lied to the FBI about his meetings with the Russians, and failed to register as a foreign lobbyist.
The Logan Act stuff was thrown around by Insane Sally Yates, but never charged. I doubt the FBI even brought it up in the plea negotiations.
Flynn’s biggest problem is he pled guilty. It’s hard to claim innocence after doing so.
Based on what we know I might have it wrong. However, I have heard reputable sources including McCarthy and Hemmingway (good journalist) as well as Sara Carter all say their sources told them that Sally Yates directed the FBI to go interview Flynn after he was unmasked and it was shared within the deep state about the contact with the Russian Ambassador. These same sources have said that it was Sally Yates who said this would violate the Logan Act.
That contact was the basis for the interview in which they said he lied. It appears to be the impetus for the whole “investigation.” There was great animus towards Flynn among many in the Obama administration because he did not agree with their worldview so it is not unreasonable to assume he would be a target. However, they needed a hook. The “lobbyist” thing did not come about until later by my recollection. That would make the underlying crime the Logan Act and not failure to register as a lobbyist.