No they cannot because it's considered idolatry. Celebrating Flag Day is thought to be similar to flag worship. Here's what the organization says.
'In the colonial days of America the Puritans objected to the British flag because of its red cross of St. George. According to The Encyclopædia Britannica, they did this, “not from any disloyalty to the mother country, but from a conscientious objection to what they deemed an idolatrous symbol.” 
There are Christians today who feel similarly regarding national flags. They are Jehovah’s witnesses. Their position is the same the world over. Being keenly aware of the Scriptural command to “flee from idolatry,” they decline to participate in flag ceremonies.—1 Cor. 10:14.