When the flagship isn't in the same sector as the miners the "mining" state immediately switches back to "idle". So I sent a flagship core with four mining ships to a sector with asteroids and told them to mine. But after a while I admin warped to that sector and the miners were still empty.
I'm getting the same results. Flagship needs to be in same sector as the drones to mine so the stationary platform idea won't work unless you remove this from the fleet before you set them to mine and reassign it before returning them to base. However, I am unsure if the drones will "remember" their docking points. Maybe they will but I have never tried.
In theory it should work but as fleet movements don't load a sector (so they can fly through stars and pirate stations unharmed) I am guessing the procedural generation of the sectors contents may not necessarily be made as a player had physically not passed through or near the sector (the edge of the 3x3x3 cube). Near spawn on a MP server where there has obviously been a fair bit of physical traffic, sectors may well have been populated with minable asteroids?
Having said all of that, when fleet mining became a reality in the game I sent a fleet of salvagers to a sector I had marked as having several asteroids. The fleet if I recall showed mining and did so for over an hour. Before I logged off I moved the fleet back to base and once in range recalled the drones to the carrier as this I had already found not to work if the fleet was not loaded. They had nothing to show for their trip which was utterly disappointing. The following session I physically went to the sector in case someone else had already mined or or they had somehow moved. An hour later my hold was filled with the remains of two or three asteroids.
As much as I would love this to be a "thing", I am beginning to seriously doubt that it is generally viable option in game. Shame really.