As long as you run enough water down the rain to flush down the coffee grounds it's perfectly fine to flush used coffee grounds down the drain if you don't want to empty them into the trash can.
I used to dump coffee grounds down the drain all the time before I started using them for gardening and I never clogged the drain doing so.
If you just take the coffee grounds that are in the coffee filter and dump just that amount down the drain every once in awhile then there's no harm in clogging your drain as long as your drain line is in good shape.
You can also just dump the coffee grounds outside onto the ground if you want too and they'll just decompose back into the soil.
Coffee grounds once in awhile work great for gardens and vegetables but if you want to dump them down the drain that's okay too but just be sure to run enough water down the drain for around a minute to flush them completely out of your main lines.