I doubt he can sue because prosecutors have immunity and that’s a pretty high bar to breach in a lawsuit. But if it can be done Sidney Powell is the lawyer that can get it done.
If the judge dismisses the case with prejudice because of prosecutorial malfeasance, he can also order the government to pay Flynn’s legal costs according to what I’ve read.
But if the prosecutors withdraw the charges, I don’t think he can recoup the legal fees.
I rather expect Sidney Powell to write a book about this, possibly with Flynn as a co-author and I wouldn’t be the least bit surprised if she took this case pro bono to get inside the case for a planned book.