I picked up what I use from the Home Depot. It is made of a heavy plastic material and reminds me somewhat of artificial turff, but shorter.
I tried a regular velcro that was self adhesive, but in the warm weather here, the glue ran a bit and it do not work that well. I am very satisified with this newer type.

If you have a large medical kit, you might need four pieces, one for each corner, but you would be surprised at how well it works.
But, I suppose it also depends on how well it mates with your rug or whatever it sits on.