How can I flatten out this wrinkly rug?

Perhaps try hanging it?

My husband used to have a carpet business, for this he would put something heavy on it with the heat/moisture in the house it would flatten out. If he was in a hurry, he would use a thick towel and steam iron to get it out fast. Put the towel between the iron and carpet and press down on each spot the length of the iron and follow the wrinkles.

Heat it up with a hair dryer and use a proper rug pad.

https://www.hunker.com/13413494/how-to-flatten-a-wrinkled-area-rug

https://www.rugpadusa.com/

no matter what u do the carpet will always slip.

Use double sided carpet tape.

13 yrs and stll stuck

Applying steam will lift the fibres and relax them into place. You may need to apply steam to the back of the rug also. A simple clothing or cleaning steamer device would suffice. Or applying hot steamy towels (not dripping wet) You can also remove the rug and reroll it for a day to get the "fibre memory" back and lay flat. Rubber pads, or painting contact cement on the edges will keep it from bunching up.

Thanks everyone. I am sure steaming on both sides will do the trick!