I would think that if your flooring was designed to be driven on, you could put the lift on top of the flooring also. The flooring will only see the weight of the car and the weight of the lift spread out over the 4 legs bottom plates. I bet that works out to be less PSI that the PSI of just the car via the contact patches of the tires.
Lets run the math...tire contact patch is usually between 25 and 50 square inches. Average car weight is 4000 lbs. So 4 tires, 1000 lbs each divided by 50 square inches = 20 PSI
4 post car lift weight is about 1000 lbs. Contact patch size is 144 square inches(12x12). So, with car, 1250 lbs per foot divided by 144 square inches = 8.7 PSI