Is asacol (mesalamine) a good treatment for ulcerative colitis flare-ups, or is it only useful to stay in remission?

Both. Asacol (mesalamine) can bring flare-ups under control and low doses can be used for maintenance therapy. This should be supervised by your doctor to monitor for any side effects and potential complications from long-term use of asacol (mesalamine).
Asacol (mesalamine) Is one of several Mesalamine formulations used to treat acute episodes as well as maintenance of remission. Sometime increasing the dose by your doctor from maintenance regimens to therapeutic regimens is needed to obtain control/remission after a flare.