It doesn't look like blackmail to me, but rather a favor to Burke. Now he has influence over his wife and additional proof of his wife's infidelity during the divorce. He probably won't get a divorce, but it will definitely untie his hands and he won't hide like that anymore.
The game says that Jaime lost his phone synced with his laptop. But considering the last time he fucked Riona, your theory about Quinn's guilt is absolutely correct. I am also sure that Quinn is behind the leaking of Cathy's photos to the Rooster. Probably the most important motive for this action is that Quinn wants Rusty to leave the presidency and Tommy to take it. But on the other hand, the brotherhood could be closed forever.
