Never get liquid or powder polish over the mechanism of a flute, unless you have it completely dismantled so that you can remove all traces. Powder residues draw oil from where it should be in pivots, encouraging the pivots to rust. Liquid polishes that get into pivots encourage rust. Powder left on a silver surface also somehow encourages corrosion - I`m not sure why.
Any polish that claims to do many different metals, especially if it includes chrome or nickel, is NOT suitable for silver, because it will be far too aggressive, and wear the silver away too fast.
I suggest a high quality silver cloth, such as Goddards. Keep to well-known polish brand names, even if they are more expensive. In the cheap products, the abrasive material is usually not graded so well, so there are coar..se(i.e. `not fine` - the stupid dirty word detector rejected the last 4 letters of the word I wanted to use!), scratching particles, mixed in with the fine, polishing ones.
Don`t such a cloth too often, just on special occasions, such as a psychological boost prior to a performance! Every time you remove some tarnish, you remove some silver.
Most of the time, simply use a soft COTTON (no polyester) cloth, or a microfiber cloth - the type used for cleaning spectacles.
Jewellers (or jewellers supplies) may sell you a special cotton cloth with a very fine pile. A very respected brand is Selvyt.
Example of a supplier:
http://www.jewelrysupply.com/noframes/polishingcloths.htm 
