I have a Yamaha flute headjoint and it is dirty. Therefore I want to clean it so its appearance will be better. Can I use a car polishing cloth for this?
I would not recommend it. The flute is silver or at least has a silver coating so a silver cleaning cloth may be more appropriate than car polish which is likely to more adjusted to gloss paint.
I once got recommended a paste intended for polishing pure metal for the keys of my bassoon.
Everything fluid has the disadvantage that you need to take care it does not reach the pads of the keys, which are easily harmed.
If it's a cloth that's impregnated, probably not. If it's just a soft cloth (for removing the polish) then, like any soft cloth, it'll be fine. I use non-abrasive polish for mine, carefully avoiding pads and moving parts, and the tarnishing - which is a sort of oxidation, I imagine - comes off.