It doesn't work like that. If you have been doing Caldari FW then your standing with Gallente Militia goes down as the attacker you are destroying Federation Frigate Destroyers. Basically If you want to flip sides you can not because your standing are to low then you have to do SoE epic arch to get the standing back up. I've already had to deal with this issue as I had to do this on my main that's why I stopped doing FW on him as it was to much drama. I was fighting for the Caldari but wanted to flip to Gallente for the Gallente LP since he is a main Gallente pilot. So basically you have to have multiple alpha's to do FW if you want to flip the losing sides
see reference
wiki.eveuniversity.org/Faction_warfare_standings
You have to be Corp-less as well. I just learned this as I added my FW-Alpha account to my hi-sec corp. She can not participate in FW unless I join the entire corp and I am not about to do that. I have enough problems with players popping my miners I'm not going to add FW try-hards to my ship destruction issues. So now I have to remove her from the corp wait 24hr stasis then she can join Militia NPC corp.