The US Military, specifically the US Air National Guard, made/commissioned the prototype flight suits, the EXO-7 Falcon, that Sam used in Afghanistan. The last one, presumably Sam's since Riley's was destroyed when he died, is the one he asks Capt and Nat to steal in "Winter Soldier". It was taken back when Sam was discharged from the service.
That suit was damaged by the Winter Soldier during the movie.
The suit is repaired and upgraded (likely completely replaced) by Stark Tech in the Stark bankrolled Avengers, as seen at the end of "Age of Ultron", and "Ant-Man". There are further upgrades, including Redwing, the falcon shaped drone, that have been seen in the prologue of "Civil War".
The computerized goggles, and the drone, Redwing, were not part of the original suit seen in "Winter Soldier".
It's never directly stated in any film, or the prequel comics for the MCU, who designed the original EXO-7. According to a now dead link (2014 cache by Archive.org), writer Anthony Breznican says:
When EW visited the set of Captain America: The Winter Soldier, I noticed that the prop wings had a small trademark embossed on them, alongside a serial number: Stark Industries.
BUT It's not visible in any frame of the film with the suit.