Hi James, as Brad mentioned I have done some recurves with a linen with a camo print under the glass.
There you can find more pictures here in the 'recurves' section
http://www.swissbow.com/ It added about 0.2 mm ( 0.008" ) to the stack, but I guess that depends also on the thickness of the material you want to glue into the bow. I can't tell you how much it has an influence on the performance of the bow, because I haven't done the same bow without it. But I think it will probaely slow done the bow a bit. Although the last one I did was a real good shooter with the appropriate arrows.
When you laminate it into the bow make sure that the linen is completely soaked with epoxy. You will need a lot more epoxy than usual, so better be prepared and mix enough of it. A lot of it will be squeced out of the bow when you press it into the form but I just whiped it off to prevent glueing the form to the table.
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Andy