To do that there has to be some explanation of why, then, he previously pleaded guilty. And, on close inspection he pleaded guilty to two separate crimes:
Flynn, on his own, could withdraw from his plea bargain, but then would have to go to trial, where his previous admissions of guilt would be allowed into evidence.
On the other hand, if he can get the Judge to dismiss the charges for procedural reasons he ends the affair with no conviction, and no need for a pardon.
I believe the argument on the first charge is: "The FBI failed to provide exculpatory evidence, so we pleaded guilty without knowing they had proof Flynn didn't lie.
The judge might buy that, he's famous for hating Federal Prosecutors witholding evidence, something he has dealt with in two high-profile cases - the trial of Sen. Stevens of Alaska and various Judicial Watch FOIA litigations against the IRS.
In the Stephens case the witholding was so severe when he learned of it he overturned the conviction he had overseen, and referred the prosecutors to the DOJ for investigation.
Assuming he could convince Sullivan that the "Lying to the FBI charge" is all based on FBI and Prosecutors misrepresenting things and hiding evidence of his innocence, there is still the Turkey lobbying issue that would have to "go away" for Judge Sullivan to toss the entire case.
That's what I think this is the start of a play to do, with the argument going something like:
I was misrepresented by previous council, who did not clearly explain the importance of willful misrepresentation (which this was not) with merely having my lawyers mis-state things on forms (which happened).
I admit I don’t know all the nuances of the law and the details of these cases, but from what I’ve seen it looks like all of Flynn’s lawyers have one thing in common: they’ve all been representing a client who is a moron.