Hi
My first time on here so 'hello everyone'. Whether or not your floor will show damp with a damp meter will depend on how old the floor is, what the stone is and how it was laid. Sure, many old stone floors were laid on earth, or old lime-mortars, but some were laid over concrete that did indeed incorporate some kind of damp-preventing layer.
Often, thin layers of slate were used as a rudimentary damp course. If your stone is a dense, native British slate or similar stone then very little moisture could pass through it in any case (although it could pass up through the joints). Even if there is no damp proofing of any kind, that does not necessarily mean you are bound to have a moisture issue.
However, you could have very low level moisture transmission - that as long as the floor is uncovered, will give you no problems. This however could change if you then trap that moisture under a levelling compound and wood floor, allowing it to build up and create possible issues.
A couple of tell-tale signs to look for are obvious damp patches, and or signs of white/grey deposits (efflorescence). If you have neither then you do not have an obvious damp problem. You can do a coupld of quick tests, if you can get your hands on an old, galvanized metal bucket/pail and fill it with cold water, then leave it over-night in a few random places and see if you get condensastion underneath it. You can do much the same thing by taping some squares of polythene down again in a few randome test areas, see if any moisture collects under the polythene. This could perhaps give you a more visual indication than a standard 2 pronged damp meter. If you can get your hands on a hygrometer from a flooring company, they work in much the same way as the ploythene - in that they trap, but then measure ambient moisture that is collected.
If you find that you do have a moisture vapour issue, then depending on how bad you might be able to put some kind of treatment on it. I used to fashion a rudimentary damp screen by using a 50:50 mix of water and a proprietary SBR bonding agent, mixed with odinary portland cement to a thin slurry, then painting it on the floor. Let it dry completely, then apply a second coat at 90 degrees to the first, then a third diagonally. Did not make a thick layer. However I am sure there are plenty of ready made preparations now available for this.
Using a good quality latex modified levelling compound will also help.
Hope this helps
Ian