At the top of the stack, if it has been capped, you could put airbricks, with airbricks or plastic vents where each fireplace has been bricked up.
Builders are very lazy people, and, when removing a fireplace or hearth, like to throw the rubble into the hole to save themselves the effort of carrying it away. This rubble tends to hold and accumulate damp, especially on the ground floor as there is no DPM under the hearth. It is best to dig it out, especially if you already have signs of damp.
You can open up an old fireplace, for an ornamental nook, or wine store, shelving, or a home safe, if you want.
Do not allow anyone who sells silicone injections into your home, even if he calls himself a damp specialist.