I air dry prints emulsion up on fiberglass screens. To flatten, I place them as mentioned above between acid free board with an interleaving sheet in my dry-mounting press with either low heat or no heat. There is also a silicon coated release paper available if you are concerned about the emulsion sticking. I only use fiber based gloss paper and suggest treating matte paper the same. Although I use glossy paper it is air dried and does not have a shiny glossy surface. I generally don't flatten unless exhibiting or selling the print. If you are dry mounting the print (which I prefer not to do) then that takes care of your flattening.

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