I didn't reallize sewing machine technology was that good in the early 1860's. In the USA most national flags were entirely hand-sewn, though machine stitching of the stripes was not really "rare." What WAS rare was the use of machines to stitch the stars.

If the flag is of the Civil War era, did it belong to the CSS Shenandoah or the USS Shenandoah?

From the US Navy Historical site. Note that the USS Shenandoah visited British Colonies where it very likely would have flown a Red Ensign as a courtesy flag:

The first Shenandoah-a wooden hull, screw sloop of war built by the Philadelphia Navy Yard-was launched on 8 December 1862; sponsored by Miss Selina Pascoe; and was commissioned on 20 June 1863, Capt. Daniel B. Ridgeley in command.

Shenandoah departed Philadelphia on the 25th, keeping a sharp lookout for Confederate raider, Tacony, as she made her trial run to Boston to fill out her complement. On 11 July, she sailed in search of Confederate raider, Florida, cruised off George's and Nantucket shoals, thence preceded toward Block Island and Cape Sable. She returned to Boston on 27 July and spent from 4 August to 8 September in the Philadelphia Navy Yard. On 12 September, she arrived off New Inlet, N.C., to join the North Atlantic Blockading Squadron.

Shenandoah spent the greater part of the next 15 months patrolling off Wilmington and searching on the blockade runner routes between Nassau and Wilmington. This cruising took her as far as Key West, Fla., and to the Bahamas and Bermuda. During a four-hour chase on 30 July 1864, she fired heavily into Confederate blockade runner, Lilian, which escaped in the darkness to the safety of Cape Lookout shoals. At daylight of 7 August 1864, blockade runner, Falcon, narrowly escaped Shenandoah and Santiago De Cuba by throwing cotton overboard to lighten load and then outsailing her pursuers in the direction of Cuba.

I can't think of any characteristic of that flag that could tell us if it was used on a USS or CSS vessel.

Nick A
Columbia MD