Make "will have been going to go" correct

The reason the phrase is never used is because "will have been going to go" invariably includes "am going to go". But in theory, if your travel insurance company asked when you took the decision about your holiday, you could reply "By the time this letter arrives, I will have been going to go (to Acapulco) for fourteen days."

Well, I can't think of an example for your exact phrase, but I can think of one with similar construction, and circumstances in which I might use it.

Example: I'm on holiday, writing a postcard to someone who I know is also going on holiday in the near future and in all likelihood won't be reading my missive until they get back from their holiday.

In that situation, I could exchange the standard "I hope you had a good holiday" with "I hope you will have had a good holiday". Yes, it's convoluted, but more temporally correct. (I wouldn't write it to a non-native speaker though).