My first impulse is to use a spring loaded arrangement where the normal position is up and a motor (and possibly light wire rope) is used to pull the flag down to the flat position loading a spring (possibly a gas spring) where it engages a sear. To raise the flag the sear is triggered and the spring return to normal, raising it quickly.

You’d need to work out a clutch arrangement so the deployment meets no significant resistance from the motor and cable on the way up. The gas springs are fast but not so fast as to make it dangerous and properly sized, any obstruction would stop the deployment with little impact. Wind loading would need to be taken into account so it would deploy even in a reasonably string wind.

For transport and storage, the spring would be attached with a pin rather than bolted on, it could be pulled and the flag made to lie flat with no tension.

 

If the leadscrew mechanism is already fabricated and functional, then an alternative control scheme can be used that will still be quite simple, and very reliable, and consume no power except while the flag is in motion.
The additions would be adding a mechanical link that would be moved one way or the other as the driven element traveled the last half inc or so in each direction. That mechanical link will operate a DPDT maintained position switch to it's opposite position as the load block reached the end of it's travel. That would provide the reversing direction for the motor, which is required. Also at each end would be a normally closed single pole switch that would operate in unison with the tripping of the direction switch, so that the motor circuit would be opened. Thus at each end of the move, the motor would be halted. Those two switches would be connected in series. To initiate motion, a relay contact operated by the remote control receiver would be closed for a time adequate for the associated end switch to be released so that the contacts closed. That will comprise the entire control scheme. Considering that the two end switches would be required in any instance, the addition of the mechanically operated direction change switch will not be so very big deal. The motor drive will need to have enough inertia to coast a very small bit after the switches operate.
No electronics, no processor to program, and no standby battery drain. The mechanical addition would not be much challenge for anyone able to fabricate the asssembly in the photo at the start of this thread.