Washing Flannel Backed Plastic Tablecloths

Sure, I do mine all the time.

I use the gentle cycle, medium water level (Just enough to cover it) and just a bit of detergent.

I put mine in the dryer on "delicate" for 15 minutes or so...it makes it nice and soft and gets the creases out.

Yep, but watch your front side when pulling it out, it can hold water in creases and douse you a good one. Air dry as it tends to get too hot in a dryer.