I have a chimney with three flues (exterior chimney on a one story house). One is for a wood burning fireplace we do use. The other two were for the furnace and water heater but are both no longer in use (no metal liners, just clay). I sealed them at the bottom in the basement (fire-rated spray foam and then plywood over the round hole). Assuming the tops should be dealt with, should I break up the clay liner to just below the concrete cap and then redo the concrete cap to cover over the holes (looking like they were never there)? If that is the case, how could I 'fill' the holes a few inches down so that the concrete filling them a few inches down inside doesn't fall all the way to the bottom?
Allow for the possibility that you or the next owner might want to use them again, and try closing them off "less destructively" - metal flashing as @bib suggests, or my personal favorite for this job, a glazed ceramic tile mortared onto the top of the flue. Stays put, sheds water, can be knocked free in the future if there's ever a need for it.