OP this is a very serious matter. A 15-year-old encouraging a 14-year-old to end her life is potentially a criminal offence in the UK, and your daughter's safety comes before her preferences about how you handle it.
You need to take charge and confiscate her phone while you act - explain that this isn’t punishment, as she has done nothing wrong, but it’s to protect her. This is not negotiable - you are the adult, she is the child and you are acting to protect her. Ideally you should screenshot or photograph the messages and see if they’re on auto-backup to cloud services, as screenshots may be there even if she deletes them. You should also make notes of dates and times, of what you've seen yourself - it counts as witness testimony.
If you think she’s in immediate danger ring 999 - that would be my go to if the messages are ongoing - alternatively 101 to report. Tell police she's being coerced into silence and may try to delete the evidence. They can usually forensically recover deleted items so at this point reporting is the main concern and worry about evidence later.
As for your daughter refusing to talk to police, it really doesn’t matter. The boy can be investigated and potentially prosecuted for encouraging or assisting suicide, and also for malicious communications - the police don't need her statement to build a case if other evidence exists, and se may not be his only victim. But you really do need to act quickly if these messages are flooding in.
Her refusal to talk to police is a red flag and it suggests he's controlling her or she's frightened of consequences for him. As difficult as it may be, you need to tell her first and foremost that she hasn’t done anything wrong and none of this is her fault - that she won’t get in trouble for anything, but she is in danger if this continues, and that his behaviour is a crime against her, not a secret between them. She is not responsible for the consequences to him of the choices he made.
You can also ring childline 0800 1111, or NSPCC 0800 800 5000 for advice on safeguarding and reporting without her consent - and how to protect her while you act. Ideally you should also contact the school , but at this point they may have already started the summer holidays.
I wouldn’t approach the parents. You have no idea how they will react and if they suspect you will involve the police they may try to destroy evidence. Your priority is your daughter’s protection, so l would let the police deal with that side of things.