Edit: Also, what was the reason.
If, by the term "military flag bearers" the OP is referring to "colour parties", they went out of use when military units stopped carrying their colours into battle as rallying points. There have been earlier discussions of the issue.
What do you mean? The flag is still carried into battle. It just isn't carried by a man without a weapon. Every soldier in the US Army carries the flag on their shoulder. Every vehicle has it painted on. The flag is in more places now on the battlefield than ever before.