Frivolous -- Frivolous can be used as a negative, but it's also quite commonly used in the context of pursuing something that may be entertaining or fun, but has no practical value -- for example, a frivolous purchase would be something you buy that makes you feel good, but that you don't actually need. People will more often acknowledge that they do something frivolously than either flippantly or facetiously, and it tends to be framed as a half-positive -- something like --
"I know it was a little bit frivolous, but don't you just love it?"
Flippant -- this is the one that's most often used critically, usually in the context where someone is dismissing something genuinely serious with a play at humor. For example, someone might be criticised for their flippant dismissal of a serious political issue.
The gentleman's flippant remarks about the Middle East drew ire from the opposition.
Facetious -- This is probably the least widely used of the three, but refers more directly to being humorous than the other two. Most often, I've heard it used almost as a disclaimer about something someone is about to say, in the line of:
I don't mean to be facetious, but...
Which is similar to saying "I don't mean to be funny", or "I don't mean to make a joke", and then proceeding from there.