No, really, go with me on this. More specifically, you are the fourth incarnation, as portrayed by the inestimable Tom Baker.
I fly high with various colors on me.
Doctor Who is well known for flying in his T.A.R.D.I.S in all his incarnations, but the fourth Doctor in particular is well-known for the multi-coloured scarf he wears.
But most of the time I sit in a corner and not fly.
The Doctor actually spends relatively little of his screen time in the T.A.R.D.I.S., as his adventures are typically on the ground.
A sling of my hair is always long enough to touch the ground.
The Fourth Doctor was well known for his long, curly hair. If one was to weave a sling from his hair (if one had a reason to wish to do so. If the Daleks were to, say, build a giant mechanised robot to threaten the world and the Doctor needed something with which to fling a rock at it), then one could be quite certain that such a sling would easily be long enough to touch the ground.
At times I have a tail.
Tom Baker, the actor who portrayed the Fourth Doctor, also was an actor in The Winter's Tale (1968), The Canterbury Tales (1972), The Tales of Aesop (1990), and another production of The Canterbury Tales (2000). He has had, in fact, several tales.
I hate rain. And I usually don't come out during a rainy day.
(See? Not a good look.)