I cannot vouch for the fact that all companies had flags. But, I do know early in the war, in East Tennessee at least. Companies upon being raised and sent off to their Camps of Instruction, were feted by their local communities and presented a flag by a local young lady.
Check out my website for the 43rd Tennessee for a picture of the flag presented what was later Co. B, of the 43rd headed by Capt. Cawood and a bit on its presentation.
The Athens [East Tenn.] Post pages record a number of these events throughout the county.