Each regiment was supposed to have a regimental flag and a national flag, but like almost all things, whether they did or not depends on the time and the circumstances. For instance, the 13th Pa Reserves were split into 2 battalions in 1862. One was on the Peninsula, the other in the Valley. The one in the Valley carried an unofficial flag that had originally belonged to one of the companies. The battalion on the Peninsula lost their colors at one point. When the 2 battalions were reunited, they marched under the unofficial flag until a new one was presented.
In addition, believe it or not, there were times when a flag was retired as no longer servicable, and there was a period of time when the regiment either borrowed one as needed or did without. The Iron Brigade was presented with a flag all its own (making it I believe one of a select few brigades which ever had distinctive colors) but they sent it home as too pretty to fly. I can point to a number of high number Pennsylvania regiments which never received flags at all.
Pine River Boys, Co I, 7th Wisconsin
"We're... Christians, what read the Bible and foller what it says about lovin' your enemies and carin' for them what despitefully use you -- that is, after you've downed 'em good and hard."
-Si Klegg and His Pard Shorty