I went up to inspect and couldn't find anything obvious. A roofer came in & hit the chimney flashing with some caulk. I also added some caulk, but I'm still leaking. I'm pretty sure somehow the flashing/chimney connection is to blame, but I can't find anything.

Should I just go up there & smear the heck out of the whole area with some kind of tar or caulk?

The flashing, correctly known as a cover flashing, is there to prevent water ingress at the point where the tiles meet the chimney, there will also, beneath the flashing, be soakers. These will be fitted horizontally underneath each tile and returned up the vertical face of the chimney.
Your flashing will be chased in approx 1" into your brickwork, and if enough rain soaks the vertical surface of your chimney then it will penetrate beyond the point at which the chased-in flashing terminates.

It's really a case of inserting a cavity tray which will extend the full width of the brickwork, the best option, or waterproofing the stack.

The step flashing goes up the masonry and under the roof material, but above the drainage plane under the shingles (often roofing felt). Larger pieces than step flashing can be used if the line is not sloped relative to the roof deck.

The counter flashing is cut into the masonry joints above the top of the stop flashing and extends down to about 1/2 inch above the roofing material.

Simply gluing step flashing to masonry WILL produce leaks (if not immediately in a few years).

Caulk and tar are not used to waterproof flashing, but as a temporary fix (at best) for failed flashing.

The older way of securing the counter flashing was by driving lead into the groove in the masonry to wedge the flashing tight.

There is Portland cement based 'caulk' available now that can be used to secure the counter flashing into its groove in the masonry.