Yes. I think
@AU Seeker is on the right track.
It's a nice piece of memorabilia, but I believe that’s what it is, rather than having seen official service. These kinds of things with fringed borders were made for sale in local shops around military bases, decorated with unit numbers and names, slogans, village locations and personal names. Some were used as local guard banners but they were mostly made as souvenir memorabilia for US soldiers to take back home. If it opens up on the side that has the pink band, then it was probably made as a cushion cover, which is commonly seen (some larger ones were also made as pillow cases). You say it was found in an inside pocket, but presumably folded up rather than being pocket-sized.
A ‘Chi Đoàn’ was a tactical armoured or cavalry unit in the Army of the Republic of Vietnam (ARVN) and ‘Thiết Quân Vận’ means ‘Armoured Personnel Transport’. These units were heavily reliant on American M113 Armoured Personnel Carriers, modified and adapted into highly mobile combat vehicles. I would assume 3/7 to be for the 3rd Troop of the 7th Squadron, best known for their role in the recapture of Huế during the Tet Offensive in 1968.
On the other side, ‘Chi Đội’ means ‘Detachment’, referring to a smaller group within the unit. I can’t read the word below, embroidered in gold, but it may be a village name, unit call sign, or even a personal name.
