ps looking at the picture i would strongly suggest a new flue liner as the mortar has probably gone from the joints inside the stack . this can allow hot gasses to penetrate the brickwork and char or even ignite hidden trimmer timber joists in floor or roof.
just for interest as a new member, I was chartered Building chappie before retired and standard stuff was three coats of aluminium wood paint (silver looking stuff) then coat of PVA as primer to aid a bond (glue bonding agent water soluble) then important, to finish, always use Sulphate...