How should I deal with the floor in my basement that has just flooded?

I’m sorry to hear about your troubles. If it’s any consolation, flooded basements are tragically common. I’d start by draining and drying your basement as quickly as possible, just to see what happens. Running fans and a couple of dehumidifiers is a good way to start. Although it’s standard practice to automatically tear out wet flooring, and it’s often necessary, I have seen situations where drying without removal worked perfectly. The trick is speed. Even if swelling and permanent damage remains, and removal of the floor turns out to be required, at least you gave it a try. If you do end up installing new flooring, do all you can to address the causes of the leak. Also, be sure to install a subfloor system that offers some protection against minor leaks. These can make the difference between a ruined floor and no damage at all in some cases of flooding.