Difference between facetious, frivolous and flippant?

These three words have nearly identical meaning. The meanings of these words according to Google are

Facetious: treating serious issues with deliberately inappropriate humor; flippant.

Flippant: not showing a serious or respectful attitude.

Frivolous: not having any serious purpose or value.

If I take these definitions, the words "Flippant" and "Frivolous" seems to be used in a pejorative sense, while Facetious seems a bit "lighthearted" type of characteristic. I am not a native speaker. Are these true of the words or am I over-analyzing similar words. Are there any differences between them?

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.

In my experience, the three words are fairly different.

You are correct that Facetious is often very lighthearted. In fact, it actually comes from the Latin word for jest. If I were to make a sarcastic joke about tearing down my house because I found a large spider, I would be speaking facetiously.

Being Flippant can come in a variety of forms. Most often, it is a carelessness of attitude. People can often become flippant in an attempt to be playfully facetious. It is used to describe an uncaring attitude. If a friend of mine were dying, and I made a joke about it, I would be speaking flippantly.

Frivolous is a term used less to describe an attitude, but more of an action, and is often used in the context of finances. If I were to spend all of my money on a guitar collection, when I don't even play guitar, I would be spending my money frivolously.

Flippant can often be used in place of Frivolous, but almost never can Frivolous be used in place of Flippant

The three words are generally pejorative. Here are the differences:

Facetious refers to speech or writing using the bite of ironic humor to address serious issues without respect — even flippantly or frivolously.

Collins English Dictionary, 12th Ed.:

characterized by levity of attitude and love of joking, jocular or amusing

Flippant refers to speech or writing that is cute, without showing a serious attitude about a serious matter. As such, more dignity is expected: When interviewing, you are better off saying you don't know than giving a flippant answer.

American Heritage Dictionary, 5th Ed.:

marked by disrespectful levity or casualness

Frivolous refers to lacking in substance or seriousness: the frivolous talk of gossip and rumor. A lawsuit brought to court for a small broken promise may well be dismissed as a frivolous lawsuit.

American Heritage Dictionary, 5th Ed.:

unworthy of serious attention; trivial, inappropriately silly