The star of David (Magen David) is
"also known as the hexagram, or more rarely, *Solomon's Seal, is long and complex. Although it is now the most common and universally recognized sign of Judaism and Jewish identity, both within and outside of the Jewish community,it has only achieved this status in the last two hundred years. Before that it was
chiefly associated with magic or with the insignia of individual families or communities"
(quoted from
http://www.menorah.org/starofdavid.html )
Although some have claimed this is the star mentioned in Acts 7:43 (KJV: Yea, ye took up the tabernacle of Moloch, and the star of your god Remphan, figures which ye made to worship them: and I will carry you away beyond Babylon.) I cannot find conclusive proof.
However, can you quote scripture where David used a star as an insignia?
The only verse I know of that is in the Bible with the words star and David is Rev 22:16 and that is not about the "star of David" at all.
According to this site of The Magen David Adom (Red Star of David); the Jewish "answer" to the Red Cross
"Q) Do we know from the Bible that David used this emblem, or is it an extrabiblical tradition?
A) The star of David is not mentioned in the Torah. (Bible)"
http://www.ukmda.org/history.html