Adding to Mudit's answer.
The answer is:
I'm needed by a doctor to travel through time:
Doc Brown needs to reach 88 mph to travel through time in Back to the Future
Or a player looking for their keys:
Piano keyboards frequently feature 88 keys and thus a piano player would look for their keys.
When on the plane where the great answer resides, I'm part of the whole Strategy:
Refers to "88", a song on the album Strategy from the band Level 42. This ties in with the 'great answer' as a Hitchhiker's Guide to the Galaxy reference in which 42 is the 'Answer to the Ultimate Question of Life, the Universe, and Everything'.
I can be found in a dead man's hand:
The card hand called the 'dead man's hand' typically contains two 8s.
Yet still, I cannot be touched:
88 is an untouchable number
In China, I may say farewell:
In Chinese, 8 is pronounced bā. In text speak, this is used as a farewell due to its similarity to the English bye. Thus 88 = bā bā = bye bye.
In Japan, I mean so much:
88 in Japanese often means "a great many" or "countless".
I have been known to have colourful wings:
The number 88 looks like a butterfly with spread wings and certain species of butterfly, Diaethria Anna have a distinct 88 on their wings.
I am about which the cool kids sing:
The band, 'The Cool Kids', have a song called '88+'
Thanks for the puzzle @hexomino!