I've always taken aspirin and neither my GI nor my doctor have had much to say about
it.
The recent series of articles on UC in the NYTimes mentions that the caution against NSAIDs with UC had been discredited. I've looked at some of that information, and it seems the biggest beefs (beeves?) with those studies is that the sample size is way too small and some of the science behind it isn't particularly stringent.
NSAIDs can cause gastric upset and may promote bleeding, and they're not particularly good for you in the long term or in high doses. But it is likely that they do not cause a flare. That's my take on what I've read recently.