Is the chimney ready?
Chimney caps need a good solid base to attach to so that they do not blow off (and potentially cause more damage.)
Flue tiles on top
These photos show a chimney with a flue tile extending out of the top of the chimney. The stainless steel rain cap screws onto the tile. The screws are machined to a sharp point so that they dig into the tile somewhat.
A worn crown can cause the top flue tile to become loose, which can then blow off in a wind storm, particularly when a rain cap is screwed to the flue tile. Animals can get into the chimney if the crown is loose or missing, as can rain.
Your chimney should look like this photo below, which shows flue tiles in good condition (not cracked) and a good, solid crown that is bonded well to the top of the chimney: