No, the Star of David — Magen David — that appears on the flag of Israel, and is often found as an Israeli and Jewish symbol for many purposes, is not explicitly mentioned in the Torah.
However, the expression “Magen David” in fact appears in the blessings recited after reading the Haftarah (which follows the Torah reading on Shabbat). In the context of the blessing, the phrase “Magen David” does not mean “The Star of David”, but rather refers to God, and means the “Protector of David”, i.e. the Protector of the Jewish People. This blessing in which this expression appears, as well as nearly all blessings, was composed by the “Men of the Great Assembly” — prophets who led the Jewish People during the period of exile between the First and Second Temples.
The Star of David as depicted by a six-pointed star, has long been associated with the Jewish People. In Southern Italy, a tombstone dating back to 300 CE was found with a six-pointed star on it. In the year 1354, King Carl IV insisted that the Jews of Prague make a flag for themselves that would feature the six-pointed star as well as the five-pointed star of King Solomon.
The words "Magen David" literally mean "Shield of [King] David." Some say that the soldiers of King David's army wielded shields in the shape of a six-pointed star. King David's personal royal seal, however, was not a star, but rather a shepherd's staff and bag. His son, King Solomon, used a five-pointed star for his personal seal.
In Kabbalistic teachings, one finds that the number six represents the Heavens and the Earth and the four directions (North, South, East, West). There are those who suggest that the Magen David with its six points correspond to this Kabbalistic idea, which in turn can represent God's Omnipresence.
An interesting footnote: the words "Magen David" in Hebrew - מגן דוד - are made up of six letters.
