Use a drapery steamer.
How to get a kink out of a rug.
You may have to do it on the back to get the kinks out and then on the face yarns to get them to settle in with the rest.
When going on top of a rug you place the felt side down leaving the rubber side facing up to grip the back of the area rug.
If the corners of the rug are curling curl them backward flatten them back out and place weights in just the corners of the rug.
This should fix your problem immediately.
I cured this by using a staple gun the pile is so deep you cant see i have stapled the rugs down.
If you pull it taught while you do this it will get rid of any kinks and makes them a lot easier to hoover.
Step 4 if your rug still won t lie flat apply some heat to it.
Put a clean dry towel or two over the wrinkled rug then put the hot moist towel on top of that then lay something flat and fairly heavy over the whole shebang i usually pile on a few more.