If (big "IF" IMHO) we are planning or willing to move Flynn, his value will peak at two times. Right now, leading up to the draft and during draft week, when teams start wanting more and better picks, and August as teams account for training camp injuries and such. Thus the increased chatter about him.
I disagree that the idea of trading Flynn will net us "nothing." I do think that it is far from a necessity. For the right deal, he'll be gone.
I also think that the FO is trying to allow Flynn to get to a better personal situation with a shot at a starting gig, but without hurting the team. They're classy, but not stupid.