Add some chalk, some water, some gymnasts hair, a months worth of dirty feet, kid snot and sticky hands. You won't have a problem at all after that!!!

I see some clubs spray honey water on their bars too.
Joking aside. I know it's a pain when things are all sliding over the place, but it will pass. You can buy stuff that goes under rugs on slippery floors, but it is pricey and I am not sure how safe it would be in a gym situation.
I know when we have had mats slip at the beam etc (for dismounts) we have bungy'ed them in place using the carry loops. Can be a safety issue when the mat shoots out from under the kids.
But as for panel mats, I guess having the other kids hold them in place is the only thing I can think of, until they get worn in.