Adding recessed lighting to ceiling fan switch
Yes, you can do this. The easiest way would be to extend the wiring from the ceiling fan box to the new recessed lighting cans and connect them the way you listed.
You could also run additional wire from the switch box to the recessed light location but running new wire down a wall would probably be harder than tapping into the ceiling fan box. From your description, it appears the feed source is into the switch box so you'd be OK, just cap of the the unused wire from the 14/3 (red from your description) to the ceiling box at both locations.