I think you can find some filling materials at bunnings, something similar to no-more-gap but use to filling the gap between skirting boards and floor (i.e. After stripping off your old carpet)

The gaps shown look no more than 5mm thick mostly, so I would address the floor, as preparing this will be the only way to get a worthwhile result.
A self leveling compound poured over the slab will rectify the surface and fill part of this gap, with the flooring p,plank doing the rest. Or opt to have a foam underlay put down prior to the board to also provide an additional 2mm. You can always install quad around the perimeter to conceal this gap, which most fooring installers allow for flex within the boards regardless. Temperature change will mean they will expand and contract, and this tolerance is Important so they don't jar and pop out. Some gap is actually required.
I would go with the first option to get the best result.

A 2 mm gap can be addressed with MaxiSil silicone or similar and look just like an expansion join

When you buy the floor, they also sell quarter round skirting.
Just get the wright size. They'll advise you