[Suicide Junkie]

The avatars are ridicilous expensive, but the empires get very high start resources, most of which are used in the construction of one avatar each.

It won't work that way. Build rates aren't affected by starting bonus.

The host has to start with an altered mod, where the flags are, say 1kt in size and free.
During the actual game, the flag components can be 100000kt in size so they can never be reproduced.
Could also use a pair of uberempires with an uberracial flag tech to build the flags (red and blue flag shipsets)

You may want to take advantage of the "zero hitpoints= immortal" effect.

Put the flags into uberships with 1mp, and make the avatars have zero hitpoints.
You could destroy everything on the avatar ship except the actual flag.

Then it would be easy to capture, and you'd use repair ships to get the thing moving back towards your base.

Note: I don't call them avatars, since they don't represent the players in the game...