First of all, good job, for catching it early, before it leads to problems. You're obviosly on your game, so forget the caulk, and put it near the top or your schedule to replace it. You want to use concrete, not mortar, give it a minimum overhang or 1-1/2" to 2", and adequate slope away from the flue. I like to wrap the flue with a piece of sill seal or similar product, to keep the new crown from cracking in the early stage of the curing process. A couple of beam clamps are handy for holding your forms in place.