As you say, the only logical answer - from what we know - is that he is saving his family from legal jeopardy. It appears that the cases he is 'cooperating with' have been referred to DoJ, not in Mueller's scope. {Clintooon? 'bama?}
As to the Logan Act - no one has ever been convicted of violating it, and there are questions about its constitutionality.
***his lawyers are the worst ever***
Perhaps pro bono currently? Flynn was insistent . . . something going on. {?}
An interesting opinion (not mine);
If ya listened to Limbaugh, sorry but he’s relevant, you learn the real story on what happened today in that courtroom! The judge knows what’s really going on. Very telling was his statement about sending an innocent person to jail, then apologized to Flynn for calling him a traitor, forced a postponement of the sentencing until March 13 2019. The judge is changing the plan.
Trump needs his foundation to fall apart because the ones that’ll be exposed now can’t point and say, look over there he’s got one too!
We are about to turn things up!