Again, I get what you are saying - but if we are using the definition above, then which of the brands such as the 21 or 60, is the one passengers most identify with and embodies the company?

Is the 21 the flagship? The 10? Tyne Tees Express? The Red Arrows? They all have the same spec (apart from the hybrid engine) as each other. What about The Crusader? The Drifter? The Waggonway (connecting with three touristy areas, providing essential local links, connecting 2 major towns and a city, serving one of the biggest hospitals and cemetries in the area, definately more vital and important to some people than the 21...).
Could passengers get to the destinations served by the 21 or 60 if they were stopped?

GNE trumpet the 21 and their other branded services too.
Is one trumpeted over the other regionwide or is it a case of being trumpeted locally? If it is locally, then you could argue the possibility of 'local' flagships.

The 723 probably wasnt a flagship, but met the criteria you put forward initially for the 21 being a flagship in that it covered the original route. It also served a massive part of the region, connecting and serving possibly more places than the 21 does.
It used the new, modern vehicles at the time too.

Im not sure a specific brand amongst so many others can be the flagship brand.
If there was one brand like the old Superliner or Expresslink brand that had decent spec, then maybe it could be the flagship.