Dr Flaherty's site shows only the crescent moon, no star.
I do not know where this flag comes from. The Ottoman flags always had both crescent and star.
But the Authority on the flags on the net is:
http://www.crwflags.com/fotw/flags/tr-index.html#his where you can find virtually any flag you may or may not need.
an easy way to make a flag from this site is: Copy the desired image, make a Copy of the image reversed by 180 degrees, put the two copies side by side, so to have obverse and adverse images, resize (my experience for 28mm minis is that the long side of the flag should have a length of abt 2-3cm, print the desired copies in good colour printer, cut and glue. for Extra detail while wet you may roll it to round pencil and voila a good effect.
Alas the warflag site has no Ottoman flag.
There might be flags made by those talented people having Commercial sites producing those fine flags we all admire in many miniatures. Alas, I do not know someone who has an Ottoman Empire flag.