Is it possible to burn things in a halogen atmosphere? Fires can burn in oxygen. But, can they burn in halogen atmospheres (fluorine and chlorine only)? I am wondering this because combustion reactions involve oxygen and carbon and other elements. But, can they burn in fluorine and/or chlorine? If they do, what color will the flame of paper and wood be in fluorine and chlorine atmospheres respectively?
They certainly can. Put some water in the bottom of a beaker, fill the beaker with chlorine gas, and drop in bits of calcium carbide. The carbide will produce bubbles of acetylene, which will spontaneously burst into flame when they hit the chlorine.

Flame colors depend on many things, even in oxygen. In general, flames in a chlorine atmosphere will probably look slightly more greenish than flames in air or oxygen, simply because the gas itself is green. Fluorine isn't as strongly colored, and flames from combustion in fluorine will be VERY VERY BRIGHT.