Paisley-born McGlynn, along with pilot Helen Scott, claimed second place in the women's B 1000m time trial at the Izu Velodrome on day two of the Tokyo Games.
The visually impaired rider set a personal best time of 1:06.743 despite only reuniting with Scott just 12 weeks ago, having previously won a silver and bronze alongside her at London 2012.
While in the C3 individual pursuit final, Fin Graham finished behind team-mate Jaco van Gass to secure a first Paralympics medal.
Van Gass took gold for GB in a new world record time of 3:20.987, with Graham’s second-placed time of 3:19.780 also beating the previous world record by nearly seven seconds.
It is a further medal success for the Strathpeffer rider, who secured a bronze at the World para-cyling World Championship road race in Portugal in June.