Flags were issued by depots that let contracts to groups of women who had professional level sewing skills. Tiffany in New York accepted orders for custom flags.
Even today not just anybody can paint a flag. It involves a specific set of skills.
Especially at the beginning of the war local women sewed flags for colorfully named companies of neighbors & relations.
tnmuseum,org Civil War Flags of Tennessee Part 2, Flag Construction & Inscriptions.
Connecticuthistory.org
Hall of Flags; Memorial to Connecticut Civil War Colors.
These articles will go a long way toward answering your question.