Flashbacks are fine, but they ought to be used judiciously. The risk is slowing things down too far and frustrating your reader. Whether you frustrate your reader is going to depend on what's happening in "the present" that you're interrupting. Are you leaving your reader on a cliffhanger to go off for several pages into the past, and does that add or detract from the tension? How long is the interruption? If it's short, it can easily be taken in stride. What does the flashback tell us? Can it be conveyed some other way that doesn't interrupt the flow? Is this the only flashback or lengthy reference to/rumination on the past? If your tone is very present-oriented, then a sudden foray into the past may feel tonally off.
CathleenT, I actually feel differently about the Prince's Tale. I thought it was very effective for Harry to see it rather than hear it from Snape. First of all, Snape wouldn't have willingly confessed all to Harry. Secondly, it would've been filtered (even more so than his memories) through his continued dislike for Harry and his continued bad attitude. Thirdly, and as the obverse, Harry would have had a very hard time accepting everything Snape said because of his dislike for Snape. Seeing the memories and having just seen Snape die made it possible for him to accept the story. Basically, their mutual antipathy wouldn't have made it possible for the story to be told and accepted in any other way. Fourth, it was an effective, visceral way for us to experience it, rather than to just hear Snape monologue about it. Fifth, it was made all the more effective and poignant because by that point Snape was dead. Last, I think it was something Harry needed to experience, think about, and wrestle with alone. If Snape had been there, it would've been all about their loathing for one another, and at that moment it had to be all about what Harry had to do next. We are cheated of the possibility of a rapprochement, but I don't know that that would've rung true, and anyway it's part of why death is so shitty: you don't always get that final rapprochement. So, er, I agree with Rowling's choice whole-heartedly. [Spoiler-tagging just in case.]