Sure, you can use the laminate flooring for the wainscot if you like it. Go to Home Depot and buy a few tubes of Liquid Nails. It comes in a tube like caulking. Buy a caulking gun too if you don't have one.

You may want to buy a small box of 3d finish nails or some panelling nails that are long enough to go through your panels and into the wall. I use one or two of these to hold the panels on the wall until the Liquid Nails sets up. You don't need very many. If the flooring is tongue and groove, you may only need one in every second or third row.

Drive the nails at an angle, towards the wood, not towards the area with no wood installed yet. It will snug the current piece you're working with, up tight to the previous pieces. Angled nails don't pull out of the wall as easily and will hold your wainscot better than straight in, until the glue sets up.

Good Luck.