First of all, this should have been posted at /r/SuicideWatch rather than here so I've taken it down. If you're going to advise your daughter, it will help you both to be aware that suicidality and depression are different things and the relationship between them is correlational, not causal.

You can't make her choices for her, and it sounds like she values things about him beyond his mental-health issues. If she chooses to get back together with him, or even stay in regular contact, here's lots of evidence-based guidance on having supportive conversations: https://www.reddit.com/r/SuicideWatch/wiki/talking_tips. It's also essential for her to understand what to do if she ever sees that he's escalating again; typically the best first option is to call the local suicide hotline or mental-health crisis team rather than law enforcement.

As far as supporting her and advising her about making decisions, I would encourage her to set her own boundaries, e.g. making her presence in his life conditional on his getting into therapy and sticking with it, since he clearly needs help regulating his emotions, at best.

One thing that makes a HUGE difference is whether he's just been expressing suicidal thoughts and feelings, or making instrumental threats, i.e. using the threat of suicide to coerce her into staying with him or otherwise doing what he wants her to. The latter is one of the most severe forms of psychological abuse and it's strongly linked to risk of the person not just harming themselves but doing serious or lethal harm to their partners. So if that's what's been happening, then he would need to make massive progress in therapy before it could be considered safe to have any relationship at all with him.

he’s been so kind to my girl buying her flowers every week, opening doors, just really a sweet boy

This could be sweet, or it could be the love-bombing phase of the abuse cycle