The Israeli Flag, like the Israeli national anthem, was a "gift" of Zionism. Since the Zionist movement, along with its organizations, became the Israeli government, its flag and anthem became the flag and anthem of the Israeli government. But the emblem of the State is from the Bible; it is a symbol Chosen by G-d; it is the Menorah.
The Israeli Flag
How the Israeli Flag was chosen:
According to David Wolffsohn, who attended the First Zionist Congress in 1897:
At the behest of our leader Herzl, I came to Basle to make preparations for the Zionist Congress. Among many other problems that occupied me then was one which contained something of the essence of the Jewish problem. What flag would we hang in the Congress Hall? Then an idea struck me. We have a flag--and it is blue and white. The talit (prayer shawl) with which we wrap ourselves when we pray: that is our symbol. Let us take this talit from its bag and unroll it before the eyes of Israel and the eyes of all the nations. So I ordered a blue and white flag with the shield of David painted upon it. That is how the national flag, that flew over Congress Hall, came into being.
Therefore the Israeli flag is a reminder of the faith and prayers of the Jewish people that have for so long cried out to G-d, that He may Redeem His people Israel. Now that the remnant of Israel has been Returned to its Land, and Jews worldwide need only pray to themselves that they should fulfill the Will of G-d, the Israeli flag should be a sign to them that Israel is where they belong. And the flag should be a reminder to Israel that it is the nation of G-d.
What is the shield of David?
"The Magen David (shield of David, or as it is more commonly known, the star of David) is the symbol most commonly associated with Judaism today, but it is actually a relatively new Jewish symbol. It is supposed to represent the shape of king David's shield (or perhaps the emblem on it), but there is really no support for that claim in any early [Jewish] literature. In fact, the symbol is so rare in early Jewish literature and artwork that art dealers suspect forgery if they find the symbol in early works...
"The symbol of intertwined equilateral triangles is a common one in the Middle East and North Africa, and is thought to bring good luck. It appears occasionally in early Jewish artwork, but never as an exclusively Jewish symbol. The nearest thing to an "official" Jewish symbol at the time was the menorah.
"In the middle ages, Jews often were required to wear badges to identify themselves as Jews, much as they were in nazi germany, but these Jewish badges were not always the familiar Magen David. For example, a fifteenth century painting by Nuno Goncalves features a rabbi wearing a six-pointed badge that looks more or less like an asterisk.
"In the 17th century, it became a popular practice to put Magen Davids on the outside of synagogues, to identify them as Jewish houses of worship in much the same way that a cross identified a christian house of worship; however, I have never seen any explanation of why this symbol was chosen, rather than some other symbol.
"The Magen David gained popularity as a symbol of Judaism when it was adopted as the emblem of the Zionist movement in 1897, but the symbol continued to be controversial for many years afterward. When the modern state of Israel was founded, there was much debate over whether this symbol should be used on the flag." (As posted at: http://www.jewfaq.org/signs.htm).
But the shield of David is a good sign for Judaism, because it is the hope of Redemption and of the renewal of king David's leadership that has given the remnant of Israel the courage to rebuild Israel. It is true that this is just a star, but if it is said to be the "shield of David" then it has a whole different meaning. This star has been a symbol for the Jewish people; one of renewal and rebirth, and of the return to a united Israel. Because ever since the time of David and Soloman, Israel has been divided in its own Land and seperated across the borders of nearly every nationality.
The Israeli Emblem
The Menorah
The menorah dates back to the beginings of Israel; it is the symbol of Israel's Role in the world. This seven-branched candelabrum was used in the Temple, and in the Tent of the Tabernacle before the Temple was built. Israel Was Instructed to build it, and these Instructions can be found in Exodus 25:31-40.
The menorah has lit up the Tabernacle and the Temple; it has given light to the Laws of G-d and has made the Ways of G-d visible to many. It is a sign of Israel's Role in the world, as Israel serves as a Light unto the nations. Like the menorah, Israel has lit up the Torah and has made the Ways of G-d evident to all. Now that Israel has been Rebuilt and all its people will be Restored in their Land, the menorah is the emblem of the State of Israel because, once again, the nations will know G-d through His people. When Israel lives according to G-d, then all mankind will see and know the Ways of G-d.
You might ask, "Why are there six braches that emerge from the sides, three on each side, rather than having a single light?" It is obvious that seven lights shine brighter than one, and thus the menorah shines brighter than any normal lantern. And it is reasonable to say that too many branches would weaken the structure, hence seven lights are a good number. But more than that, the seven lights probably stand for the seven days of the week; the central light representing the Sabbath. Thus the six branches shoot forth from the central light, making the lamp much brighter, while the central light serves as the base of the structure, supporting the branches and balancing the weight of the lantern. Such is the role of the Sabbath; for Shabbat is the source of support and balance for the rest of the days, and the foundation upon which the whole week is built and from which the days emerge.
The Olive Branches
There are two olive branches surrounding the menorah in Israel's emblem, one on each side. I don't really see a need for these olive branches except that they look nice. It was chosen to include these branches because the prophet Zechariah saw a vision of a menorah flanked by two olive trees (Zechariah 4:1-14), and an angel of G-d told him that this vision stood for the Spirit of G-d, that not army nor strength could defeat, with the olive trees being the two annointed men (the king and the High Priest) that would stand by G-d when He would Rule over all the Land. Meaning, Israel would be Restored to G-d's people and the Temple would be rebuilt.
But this prophesy was not for our time, and it has already occured long ago, during the second Temple period. If the Jews want a return to that time then perhaps they want to repeat the same mistakes that have led to our decline. Israel today must distance itself from the foolishness of its past, and thus I see these olive branches as pieces of litter that don't belong. They are like the Talmud and the Mishnah, that hide the Light of the Torah and conceal the True Purpose of Israel.