I assume that the basement is below grade and is concrete, correct? Since you’ve already been flooded at least once, I’d also assume that this will occur again in the future.
In my experience and knowledge there is not any type of coating the will genuinely not fail with the incursion of groundwater or moisture in a below grade basement. The last product that I used, and had fail, was USG’s DRYLOK® Extreme Masonry Waterproofer. After about a year there were a number of small bubbles and blistering on the exterior walls of the basement mostly near the bottom by the uncoated floor.
I would consider something like indoor outdoor carpet tiles if I had the desire for padded or rubberized flooring. Whatever I did, I would assume that there will be another flood and just accept that things might get wet.
If it is just an esthetic issue and no real need to cushion the floor you might consider using concrete acid stain. Since these cause a chemical reaction with the lime in the concrete they are very durable and do not “seal” the surface and attempt to resist the hydrostatic pressures that some type of coating would endure. They allow moisture to migrate through the slab.
If you have “deep” pockets, you might consider a product like Greatmats. I have been in a couple of basements that use similar products and they were quite nice.
My current basement, even after all of the proper waterproofing and drainage systems and pumps, still had some water incursion. The “final” solution was to pour a capping slab and the basement has been dry since 2002. As long as the pumps continue to operate when the groundwater is high all is well. I did get advice, after initial construction, that no one puts a basement in a house on the valley floor. Hey, it seemed like a good idea at the time and I don’t really regret it.
Good luck with whatever you decide.