I'd guess the seal was applied on the raw cloth, before the sewing was done, so it most likely defines the manufacturer of the cloth.
At this era there was plenty of cotton production in the States, so why would anybody bother to import some from an Arabic country?
I sent a request to have a look at the pic to a friend who is an Arabic professor.
Sure it can be anything from anywhere.
I would like to belive that modern science could determine the origin of the raw material?
I'm far from an expert, and don't speak or read/write Arabic, but I have seen a good share of Arabic writings and for my uneducated eye this seal just doesn't look like Arabic.
For example, there are none of those many dots so common in Arabic (some of them indicating vowels). Next, Arabic is written from right to left - does this seal look like reverse written? Not in my eye.
And then on the first glance I would think to recognize some Latin/modern letters, like a D or F at the beginning, and a & near the middle.
Would make perfect sense, if the seal would shortcut the companys name like X&YZ.
OK, thats just my wild guess.
Finally had a chance to meet my Arabic prof. friend these days, and he confirmed that to the best of his knowledge this is not Arabic.
Nor any other of the many foreign, Middle- and Far-East languages he knows of.
I would guess thet the museum that has the tent on display would have a ways to get an analysis (Gen analyses?) about the cotton itself which could maybe tell the origin of the cotton, if it was Egyptian or US or any other, but when looking at the woven cloth I would guess that this was made with a decent machine that might not have been available in Egypt at this time.
There are actually 2 of Washington's tents remaining from the war. The Smithsonian has one & Valley Forge National Historical Park has another - I can only assume this one is the Smithsonian's, as it is no longer on display at the National Mus. of American History. I have not yet been to this new museum.
Other presidents who camped in tents would include: Jackson, W.H. Harrison, Taylor, Pierce, Grant, Hayes, Garfield, Arthur, B. Harrison, T. Roosevelt, Hoover, Eisenhower, & Truman....perhaps more
Be Prepared