I can't be 100% sure without seeing your floors, but I suspect that someone has put a coat of polyurethane on top of a wood finish that has been maintained with either wax or an oil-based soap like Murphy's Oil Soap. This would keep the urethane from adhering properly, so every time you scoot a chair, or turn, or bring the dogs in, it scratches and peels.

Will it peel off with your fingernail? If so, the only actual solution is to get the new finish off. The usual recommendation of most professionals is to SAND the floor down to bare wood, and refinish. Messy and expensive. There is another way, but most floor people don't want to do it, as it's too time consuming, but I can talk you through it if you want.

I'm not an installer, so I can't really help you with the cost of a kitchen floor, but I can help you choose something that will wear well and look nice with minimal care.