It is possible I believe, to have a flag that can be picked up. But you won't be able to see the unit carrying it.
All you need is a trigger that states: When a unique unit (only 1 on map)(example: Hero) steps on the same tile as the flag, the flag is removed. This trigger activates another trigger that states when the Hero walks back to base (to a specific location), the flag is created. This way, you can "pick-up" a flag and bring it to another location.
Here is the trigger formula:
Trigger Looping: No
Trigger Starting State: Yes
Condition: Bring Object to Area (Hero to Flag)
Effect: Display Instructions (Player 1 has picked up the flag)
Effect: Remove Object (Flag)
Effect: Activate trigger (Next trigger)
Trigger Looping: NO
Trigger Starting State: NO
Condition: Bring Object to Area (Hero to base)
Effect: Display Instructions (Player 1 has returned the flag)
Effect: Create Object (Flag)
The only down side is that you won't be able to tell which unit is carrying the flag.
The rule is that it has to be a unit that there is only one unit of that type for each player. If you set it to be a unit which there is plentiful of, all you would need to do is put one unit on the flag, and then keep a different unit in base and the same effect would happen.
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