I found interesting information about Stars of David on "flags of the World" website:
1. First Star of David flag
Dov Gutterman wrote that in 1354 the Jewish community in Prague put the Star of David on its flag and that's the first recorded appearance of a Star of David on a flag.
2. Druze soldiers' Star of David flag
Dov Gutterman wrote that Druze soldiers in the Israel Defense Forces (IDF) have a flag with a white Magen David on a green triangle.
3. Birobidzhan Jewish Autonomous Region Star of David flag
Muhamed Mesic wrote that one of his friends saw a strange flag hanging from the windows in Birobidzhan, and it includes a Magen David in the center.
4. Proposed Jewish Flag for Sweden
Natan Zlotnik designed a yellow badge on a blue background and expressed his wish to fly it at Jewish holidays.