Vinyl flooring, I normally use them in laundry rooms but I can recommend vinyl tiles which have nice patterns.

OK...let's be clear. NOTHING can withstand flooding several times per year. Even porcelain tile on CONCRETE slab will eventually have an issue. Your best bet = putting money into the water mitigation project. That means down spouts, roofing, grading the yard, adding weeping tile and french drainage system ALONG with exterior water proof membrane.

Once you have all that in place, you will be able to have whatever you want. Until then, work with sheet vinyl (super cheap). It is cheap to buy. It is easy to install (professional install) and easy to take out when you need to redo the basement because of the lack of water proofing and water mitigation.

You can water proof the kitchen floor painting on the waterproofing. Putting down a membrane including up behind baseboard is even better before putting the floor on top. I know you don't want tile, but 1/2 inch color body PEI 4 porcelain tile with a rectified edge allows for a very thin caulk line between tiles and along base of the baseboard. 1/2 inch has much better breakage strength and PEI 4 does a better job keeping the pattern.

Nan Kni 4 years ago so I am fairly certain they have finished the project by now.