What I have done in the past when I soak a photo out of an album or have cleaned them is the put them between two sheet of higher stock (thicker) computer paper in a book and apply pressure, and change it out every minute or two until the photo is just about dry, then run a cool air hairdryer over it just to the point where it is not sticky anymore, then put it back into a few fresh sheets of computer paper in a book and let it sit for a while.
If it is a press photo it will have a bit of a curl to it, but it wont be too bad and will lay flat in a semi-rigid holder or Mylar sleeve.
BTW, Old Auction catalogs are AMAZING for the weight need to flatten photos out. They are more dense than anything else on the plant, I think they break laws of physics honestly but I have not confirmed this
