The determining criteria will be how much information the reader needs. Generally you want to use flashback for a few reasons.
1) Need to know protag and/or context for emotional impact. A battle scene may not make much sense to the reader/viewer if you open with it: Everybody in it is a stranger, the reader doesn't know or symapathize with your character, doesn't even know if she is the hero or villain, doesn't know the cause or stakes of the battle. It is JUST action, and action without stakes or investment can be boring or confusing instead of exciting.
Who are these people and what are they fighting for? To tell them that you would need all kinds of interrupting explanatory BS in the midst of battle, and in movie or book, that is just bad writing. The flashback solves this by letting us get to know the protag for a bit, sympathize with her, and then we have some context in this battle.
2) Need to hide information from reader. This can be similar to reason (1), but we may want to intentionally NOT reveal information that will come out in the battle. In the battle we may reveal the hero we have come to know for a chapter is not exactly who we thought she was. She is lying about her actions in battle, she is not the innocent bystander we thought but a merciless killer, not the soldier following orders but a commander on the field. Or vice versa; she has lied to other characters in the book about her role in the battle or who she is or what she has done.
3) Importance ranking of reveals. This is more of a writing strategy. Whatever first conflict your story opens with is generally more important to the whole story than subsequent conflicts. Both battles and love stories are conflicts; which one is more important to the whole plot should be found first. So if the bloody battle is necessary, describing it physically after the love life begins makes the bloody battle a secondary conflict, perhaps a complication, perhaps just an explanation of our hero's psychology, even though it is temporally out of order.
Putting the bloody battle before the love conflict does the opposite, it seems to the reader like something that should be resolved, and if resolved too quickly then it is disappointing to the reader; a head fake. You gave the battle too much prominence by putting it first; getting your character known to the reader is more important, getting the romance underway is more important, then whatever it is the battle explains about the character and complications of the romance can be told without the reader mistakenly thinking this story is about battles.
On a related note, most (highly rated) movies and books begin with "establishing shots/scenes" where very little conflict is going on. Neither battle or romance. This is for the audience to get a feel for their hero, what is being "established" is the every day world of the hero before that world changes forever. The audience/reader must identify with the personality of the hero first or nothing the hero does is care-worthy.
This is not to say you should not begin with conflict: It just needs to be clearly inconsequential conflict. In "When Harry Met Sally", the two romantic protags are introduced and immediately in philosophical disagreement, but this is just a verbal, funny, sometimes frustrating conflict. (they are "in a box", i.e. sharing the expenses of their long car trip prevents either from walking away from their temporary partnership out of philosophical irritation).
How characters respond to conflict reveals them to the audience. It is valid advice to begin with conflict (and have conflict everywhere), but character revealing conflict, not high stakes life-and-death conflict like a battle. Many beginning writers get confused by this and use the easiest conflict to write: A physical fight. But the high-stakes fight falls flat when we don't know the stakes, or the characters or have any reason to care.
In general, save your battle for physically later in the story, when the reader wants your hero to live, and hopefully wants the villain to lose (even if that is not how the battle works out).
Also there are alternatives to flashback. The hero can reveal what happened verbally, in conversation or interrogation.
Is the battle necessary? The battle is only necessary if something in it has specific ramifications to the plot line. Just "I've killed many men" is enough to cover the emotional impact on the hero of the battle; i.e. just a few lines of dialogue can do the job, you don't need a scene.
If there is some specific action we need to see (e.g. in battle rage she intentionally kills somebody with valuable intelligence she knew she should not have killed, or she made a mistake and unintentionally killed a child and this haunts her, or she impulsively disobeyed orders and got her comrades killed, or took an impulsive risk that got them killed, our hero was a coward and NOT a hero in this battle like everyone thinks, etc).
Some things need to be shown, not told, and vice versa. It depends on the pacing of the story, and whether you can afford to interrupt it for a whole battle scene, and it depends on how important the ramifications or consequences of the battle are: if they are big and plot-changing, show it. If they are more general information (our hero has experience in battle) use a short version to refer to this un-shown battle in dialogue, not flashback.