My understanding of the Star of David is that it became iconic around the same time that Kabbalah and the Zohar began to gain acceptance as a input into Halacha. It is in the Merkavah literature and the Zohar that the 6 pointed star is given significance. The Star of David is seen as the star that connects the sephirah of Malchut to the 6 sefirot above it. Malchut is a sefira that is associated with King David.
An interesting note regarding the Star of David is that in Lurianic Kabbalah the seder plate is placed in such a way as to create two overlapping triangles. As per Gershom article where he tries to claim that it does not say such a thing. It seems that this practice, and the subsequent creation of Seder plates with this symbol is what spearheaded the Star of David into it's Iconic status.
It would make sense that a symbol used on Pesach would be able to overcome the traditional Jewish Symbol of the 7 branched Menorah.
There are many other numerlogical and structural signifcances of the symbol which give it a meaning of protection and a uniqueness to the Jewish people. (even though it's used by other cultures as well.)
The "shield of David" then grew to be understood as a literal symbol which King David bore upon his Shield (and the Maccabees) and became iconic as we know of it today.