In fact, each of these narratives was not only extended forwards but also expanded sideways. In other words, we learn more about the Polesotechnic League than just about van Rijn, or even about his protege Falkayn, more about the Terran Empire than just about Flandry, or even about his adversary Aycharaych, and more about the Time Patrol than just about Everard, or even about his protege Tamberly.
Regular readers will know that the League and the Empire were fitted into a single timeline, as the History of Technic Civilization, whereas the Patrol guards an alternative timeline, in the separate Time Patrol series. With the benefit of hindsight, we might have preferred if all three series had been unified. However, Everard operates in historical, not future historical, periods and interacts with the Roman, not the Terran, Empire. Thus, even if the few futuristic references in the Time Patrol series had mentioned the League or the Empire, there would not have been a lot of overlap.
If a proto-series is a single work, then a series is at least two works. In this sense, the Flandry series is followed by, and the Technic History is ended by, one series and three proto-series:
The Game Of Empire is a proto-series about Diana Crowfeather, Flandry's daughter;
"A Tragedy of Errors" is a proto-series about Roan Tom, a star rover during the Long Night;
The Night Face and "The Sharing of Flesh" are a short series about the Allied Planets;
"Star Fog" is a proto-series about Daven Laure, a Ranger of the Commonalty.
Flandry cameos in The Game Of Empire but the last novel about him is the previous volume, A Stone In Heaven, which, I think, deserves further attention for its presentation of the now fully matured Flandry.
Earlier in the Technic History, "Wings of Victory" describes first contact with Ythri during the Grand Survey. Thus, it is both a Grand Survey proto-series and the opening Ythrian story.