If you encounter people who say Israel nor her citizens are Zionists, then it could be that they have a slightly different definition of what Zionism is. Some people define Zionism as "establishing Israel" whereas others include "supporting even after establishment" in their definitions. That makes it a debate over past and present considerations, and that can change how people define a lot of things Israeli.
With either definition, the Israeli flag is still a Zionist flag because it represents the unifying belief of all Zionists: The establishment of Israel, with the flag being present to represent that nation. Perhaps you can argue that Israelis are in a post-Zionist society, especially if you define Zionism as a done thing when Israel declared independence, but the flag still harks back to the unambiguous Zionists and their goal of establishing Israel.
With the Star of David: It represents the Jewish religion, which is rather important in an Israeli context. Specifically, many people link it back to David, the King of the Jews, and view it as his symbol. Actually, to many of the ancients it was the Shield of David, and remains so in Hebrew to this day. That may change your view on it if you are linking it to the Illuminati, which seems to be implied with the implication that it's pyramids and not simply triangles. There are many interpretations and theories as to why the symbol is what it is, and I'll point out that the symbology shouldn't be so narrowly linked to them. For example, it could be more related to the union of male and female using ancient symbols for such (up triangle = male, down = female) or it's possible that it has more to do with the alchemic symbology of water and fire. Or it can just be their sign and that's just the end of it.