Phrase Methuselah had (flipping pompous way of referring to himself) (5)
I believe the answer is:
idiom
'phrase' is the definition.
(an idiom is a phrase or saying)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for idiom that I've seen before include "Peculiar term" , "characteristic use of language" , "Eg, over the moon" , "Manner of speaking or writing" , "Expression that's characteristic of particular group" .)