Early and pre world-war two in many countries, flags were used for signals and communications, or for identifying a parent unit. The practice fell out of style and necessity as the advent and proliferation of radios increased, and more subtle ways of identifying a commander's tank (such as a stripe painted on the turret) became more common. In most cases, units would go out of their way to mislead the enemy as to whom was the commander; either by tying down 'whip' radio antennas, or installing dummy ones on every tank in a formation. So yes, needless to say, flying distinct flags was a double-edged sword. It made for easy communications without a doubt; but allowed for enemies to identify formations (a key step in intelligence gathering) easier.

The tradition of using flags to identify tanks and armored fighting units in the immediate pre-radio era is directly tied to the usage and tradition of cavalry pennants in the pre-mechanized era. Many nations viewed Armored Fighting Vehicles as the successors to horse cavalry in role and employment, and thus many traditions of the Cavalry were cannibalized. It is however a bit less plausible for the USSR, and I find no evidence of flag usage in the USSR for unit identification; though I recall reading somewhere that the early USSR tank formations used alternating red and yellow flags to signal and communicate; pretty standard for the time. Flags remained in use post war in most Western countries only on the range.