Chimney Pot Been Cemented Over

There should be a vent at the top and bottom to allow the air to circulate without this it could cause the chimney to sweet leaving damp patchs on the the chimney wall

Fix a cowling on the top it's made out of concrete and has holes around so the chimney can still ventilate

Any redundant flues should be vented, so as to allow a air flow, so as to prevent damp, pot and venting cowl or air bricks

A lot of people do just that , I personally would have put 2 vented bricks 1 for each chimney in to prevent any damp . Most importantly I would have swept the chimneys first just to make sure there’s no nest or nasties up there (I’ve had 2 nests this week) which we can help you with , you could block up the bottom with plasterboard then again with a vent so warm air goes up the chimney or you could buy a chimney balloon or a chimney sheep to put in the flue