Usually in this situation you cycle the leadership to use the flagship. You can leave a corp and keep the flagship but you can't re-join a corp while still in it.
However for many tasks that don't involve a team of evils you can still manipulate the game to take advantage of this. For instance if the best ship for doing buy downs is the FlagShip, then you cycle the leadership to take advantage. So good for solo evil work, or colonising, or anything requires one person to do something in the flag at a time. You can have a team of people on a planet in personal flagships and have the planet defenses turned off. That can be useful but also dangerous...
A couple of HHT's back we had to do this on a daily basis but it easy to do as it was a MEGAROB game and we had a mixed corp that wiped our experience to zero each extern. So we cycled who was the leader for buy downs by manipulating our experience i.e. cost very little to get to 5 exp, someone does buy downs, then next person went to 6 exp, became leader et. Once all turns used, Evil would do mega robs and get HUGE exp however we did this just be EXTERN.
1st: Understand how how corporate leadership is passed on. If the CEO quits the corp, the person with the most experience gets the leadership and therefore ability to xport into a flagship
2nd: People will need to leave the corp - so if you have a mixed corp then take note whether you corp alignment is positive or negative (view corps by rank). You can only join a corp if on the same alignment. So if Evil aligned, you need to be evil to join.
3rd: Take note when that person quits to give up leadership, you alignment changes AGAIN, so suddenly it might swing your corp from good to bad, and you can't join back
DO THE MATHS.So to get a player into a Flagship make sure they have the most experience. Get the leader to quit while in their flagship already. That person is now leader and the other person can join.
Works best where you can cash effectively solo - if you need it to do team SDT or similar, not going to work. However it might work out that being evil in a 255 hold CEO Flagship and doing solo SDT is better than team SDT in a 150 hold ship.. SO DO THE MATHS.
If there is no death limits you can also burn turns at midnight and CBY or get murdered to help re-adjust experience and/or alignment to manipulate the system.
Have fun.. it's great when it works.. but sucks when your stuck in your home base in a personal flag ship and can't join the corp or move due to your old corps cannon and figs having you on lock down