If the pointing looks in poor condition, yes get it done.
You will need a roofer/builder to get up and check it all out, as could also be lead flashings, soakers or broken tiles.
Also check, if you have open chimney pots, get some rain guards fitted, dont seal of any redundant flues as they need to be ventilated, top and bottom.

In reply to your added info.
It sounds like your builder has diagnosed the problem, the price seems alright.
I would just add, to ask him if he is giving a gaurantee on the damp proofing.

Hi, it could be a few things, lead flashing, soakers or flaunching. Or as you say, pointing. Put it on here and let a roofer have a look. Free estimates!!! lol.

it may need pointing but if you have flashing around your chimney its more likely that will be your problem , try puting a cowl on top to . paul

hi martin here wall sounds like it needs re pointed or flashing may be burst best regards martin mm builders

dificult to answer this without looking at the chimney,could be a few differant reasons like bad pointing,flashings, broken roof tile.

Hi, all good responses,
age of the property would help trades give you good advice!
I have seen penetrating damp from old brick on a stack cause dampness, even re-pointed with new flashings & soakers.
A good quality builder you can trust is your best option.

Regards Chris