Seems territorial to me, marish flirting is a different reaction.. I would ask your barn owner if you can put up a strand of hot wire. Otherwise you'll have to teach her manually.
Basically she needs to learn to "get along". That stall is your territory, and that horse is part of your territory too. First I would wait until the other horse is gone, and see how she reacts when you go into her stall with food. Is she aggressive towards you? Does she crowd you? If she acts this way when you try to feed her, she needs to learn some manners.
If she seems okay, I would halter her and march her back and forth against that side when the horse is around. If she makes a fuss I'd make her do a bunch of circles.
If she still doesn't do anything, I would plant my butt out there all day if I had to. I'd sit and wait until she did something, then throw a lariat at her butt to get her to move off the fence. And I'd be forceful about it. You do that once or twice really hard and she'll stop. But if you nag her she'll just treat you like that horse.
Dunno, just some food for thought. That's why I hate pipe corrals.
EDIT: Electric fences aren't cruel. They get shocked once, then they never get shocked again. It's a safety issue. Would you rather her get one little shock or end up with a broken leg?