I can't look at the PSD right now, but generally speaking I use a greyscale texture overlay for flags, using a color blending mode such as "burn." I always suggest experimenting with the different modes available, as each behaves differently and could be exactly what you need to achieve the effect you're looking for. The strength of the texture can be adjusted by that layer's opacity.
Also I should note, I never start with pure white as a base color, or even greyscale. An off-white (e.g. around RGB 235, 230, 220) usually works better. Some blending modes will wash out what's beneath them and could require an even darker start.
Lastly, it often happens in flags and sails that what works for one design element doesn't work for another. The solution: use a different texturing layer for different parts of your design, clipped to affect just that part. E.g. if your eagle is in its own layer, you can select it with the magic wand tool and then switch to your texture layer; then either cut/paste your selection into a new layer, or "promote" it to its own layer. That way you can ensure the base flag is textured, without necessarily overwhelming the eagle (or vice versa). (This last trick applies to weathering as well.)
Hope that helps. Happy drawing!
