Why don't Jehovah witnesses say the pledge of allegiance?

Flags are often used as representations of things. The Bible tells us to...

..."Flee from idolatry." (1 Cor. 10:14)

...and to "Guard yourselves from idols." (1 John 5:21)

True Christians strive to maintain neutrality as regards to political factions of the world. They are counseled to worship only Jehovah God of the Bible and to give their full support to His Kingdom:

"In reply Jesus said to him: `It is written, "It is Jehovah your God you must worship, and it is to him alone you must render sacred service."' (Luke 4:8; see also Dan. 2:44)

For more, see
Why Don't Jehovah's Witnesses Vote, Pledge Allegiance Or Support The Military?

Worship That God Approves

What Is God’s Kingdom?