Electrically any cable should have an earth at every point of use, however this is in relation to fixed wiring. For a plastic lamp the wiring does not need to be earthed, though if you are using any metal fittings then these would need to be earthed.
Use two core flex it will be OK.
The link to Screwfix that advertises a loop in batten holder does not show the picture of the loop in batten holder as shown by Roys above it shows a basic batten holder. The loop in batten holders have a plastic base that mounts onto the wood and separates the terminals from the wood. The sheath of the cable should be inside the batten holder.
Not that it would be too much of a problem in general but strictly enclosures of terminals should not be flammable. I would expect a decent piece of wood would be more resistant to heat than a piece of plastic, however the flame retardants in the plastic would mean it would not continue to burn, unlike the wood.
The final connection would be from the first lamp holder to the plug and very likely to be under significant strain at times, the cable should be securely held (as by a correctly sized P clip or cord restraint clamp) in place to prevent the wire pulling out of the batten holder..