Gordon, 22, has signed his first full-time deal with the Warriors after impressing on a partnership contract with Currie Chieftains, putting pen-to-paper on a deal that will keep him at the club until the summer of 2021.
Born in Rotorua, Gordon qualifies for Scotland through his grandparents and was part of the U20 squad that finished fifth at the 2017 World Rugby U20 Championship in Georgia.
Also included in that squad was fellow back-row Flockhart, with the Inverness native signing a one-year extension to his contract at Scotstoun.
The 21-year-old made his professional debut for the club in November 2018, appearing for the first time in a 29-20 win away to the Ospreys.
A talented athlete who won national medals in shot put and discus in his youth, Flockhart signed his first professional contract ahead of the 2018/19 season.
Flockhart spent the 2017/18 season with Stade Nicois, as part of Scottish Rugby's performance partnership and was a regular feature in the team that won promotion from Federale 2.
Glasgow Warriors Head Coach Dave Rennie said: "We're rapt to have secured the services of two outstanding young back-row talents.
"We've been hugely impressed with what we've seen from Bruce and Tom this season, both on the park and in training, and they'll be crucial players for us next season in a Rugby World Cup year."