There is at least one canon reference to a phaser beam being blocked by a substance with mirror-like qualities in the Voyager episode "Phage".
Under normal circumstances this shouldn't work (even in the real world a mirror would be largely ineffective against a moderately powerful laser due to the imperfections on the glass and the absorbency of the silver material) but because these walls can "reflect directed energy" it somehow seems to work.
TUVOK: The phaser beam would ricochet along an unpredictable path, possibly impacting our ship in the process.
JANEWAY: All right, we won't try that.
CHAKOTAY: Well, maybe we should. Tuvok, what would happen if we reduced the phaser power level to a minimum setting and sent out a
TUVOK: The phaser would continue to reflect off the bulkheads until it encountered a non-reflective material.
CHAKOTAY: Until it encountered a non-reflective material, like the real alien ship.
Moving waaaaay down the canon, the only other mention of silvered armor or a reflective hull in a trek property seems to be in the Star Trek Online game. One of the MACO shield upgrades creates a reflective surface.