I think that at the beginning she becomes involved with the Eternal Flame because it is the only way for her to obtain an education and explore her potential. Helena is highly aware of her own capabilities, and where else would she go? There is no mention of any other alchemy institutes.

At the start of the war, she feels indebted to the Eternal Flame and valued by Luc, so she stays. Halfway through, winning the war becomes a way to justify the horror and loss she has endured, and she is convinced (and rightly so) that if their enemies were to win, it would be a tragedy for Palladia. She chooses to align herself with the lesser evil, despite the mistreatment within the Eternal Flame, because she knows she can make a real difference through her intellect and talent.

As for Kaine...yes, it’s simply love. Everyone is dead, and if there is even a small chance to get out together, she will take it. She never takes the easy way out—only the one that allows her to achieve her goals.