What is the best flooring to use to prevent slipping?

Linoleum and tiles can get slippery depending on what you wash with. They aren't as slippery if you just use vinegar water. Are you looking to replace your flooring?

What type of flooring do you have now? Any floor has the potential to be slippery when wet. If your dog has accidents, I would use a vinyl product.

We, too, have slippery flooring and a disabled dog. I have used rug runners for traction. If you get them small enough, it may be possible to throw them in the washer. I take mine outside and hose them off with some water, then soap, then water. It has worked for us.

Rug through rugs

Our dogs would slip on our wood floors when their nails got too long of the hair between their pads got too long (both were poodle mix) . Their pads are pretty grippy so if that's the case with your dogs maybe a groomer can show you how to trim between toes and you can use a grinding tool (I used my wizard rotary tool with a sanding disk) to keep their nails short.

you can get a rug gripper to put under the throw rugs, keeps them in place.