How to remove wrinkles from a polyester or nylon flag?
You can use a clothing steamer and you can hang the item flat and apply gentle steam to the wrinkles until they flatten and relax.
Your second option is to hand or machine wash cold and then hang dry it. The washing process should take care of the wrinkles and by hang drying it flat, there should be no wrinkles. But first of all, you should make sure that the flag is color safe.
Check that by rubbing a cotton swab on the flag colors. If it colors the cotton swab, the flag is not color safe. Do not wash it.
If your flag is color safe, you can use the washing method regularly.
But, a garment steamer is also a great idea since they are great for getting wrinkles out of clothing without needing to haul out the iron as well. Which is great for wardrobe use.