Chimney Crown Construction

If the crown touches the terra cotta flue tile, yes, it can cause both the crown and the tile to crack from hoop stress as the tile expands. Also, the tile will elongate. If its bonded to the crown, the whole top of the chimney can tear off including several courses or brick or CMU block. The ideal crown has a Sheetmetal bond break with the top course then forms set to cast a concrete pad with a min. 2" overhang. You can use forms that create a drip edge in the overhang or cut one yourself with a mini grinder. The forms need to give you a min. 3.5" thickness at the drip edge. It must slope up 10° to the flue tiles. You may need to extend the flue tiles. In any case, they should extend above the finished crown 2-4" max. Wrap the tiles with ceramic fiber or mineral fiber insulation about 3/8" thick. This will create a slip/ expansion joint. You can use #3 rebar (3/8"), 6"x6" welded wire, or even just polypropylene reinforcing fibers. You can buy this type of concrete premixed. Mix it very dry and let it mull about 20 min. before adding only just enough water to place it. The only admixture I recommend is air entrainment, which you get with a type 1A Portland cement. If you're mixing your own concrete freestyle, volcanic pumice makes for a great pozzolan as it has mysterious properties not fully & ridge understood that make it last. Let the concrete sit in the forms as long as you can as this makes it harder and reduces cracking. Of course, you'll have to oil the forms as a release agent. Make sure once you pour you work your trowel down the sides to get the aggregate away from the edge so you end up with a smooth face. I will correct myself there is a Powdered Water Repellent chimney contractors use that makes the concrete inherently water resistant. The fibers stop surface bleed so you don't get those micro channels from bubbles rising. Once you strip the forms you can use a polyurethane caulk around the expansion joint to keep out water. You can install individual flue caps or a large multi-flue cap. If the budget allows, get one of these with an outside mount as this forces the lid to move the drip line further from the face of the chimney. There are special drip edge treatments available and these caps can be made with standing seam hip & ridge. You'll want the 18ga. ss mesh tall enough to clear the flue tile by 5" min. You can get these caps in copper or powder coated ss. Most come with a non-expiring transferrable warranty.
Or, you can just coat the crown with an elastomeric product and rebuild the top of the chimney in a few years.
Regardless, have the exterior treated with a water repellent that is 100& vapor permeable. (high perm rating).
Those are the basics.
FYI, the foam you described is combustible and will break down from the ozone and UV . Silicone is the worst. I hate it. Also it's not intended for joints wider than 1/8" and doesn't fully cure when laid wide. You really should have a level II inspection done on the chimney first including a video scan. No sense wasting money on the crown if the rest is rotten as most are. Plan on a type 316ss liner for the coal. Coal would negate a copper cap btw.
HTH,