Is it permissible for the girl's father to perform Salatul-Istikhara, and for other people to perform it, despite the existence of a relationship and flirtation between the suitor and the girl before marriage?

The questioner must repent to Allah Almighty for his relationship with the woman by immediately severing the relationship, regretting it, and resolving not to return to it. Indeed, the transgressions that occurred between them are not permissible by an intention of marriage or love. The Istikhara prayer is prescribed for the woman's family to perform for her suitor, but it is not permissible for them to delegate others to perform Istikhara on their behalf. A person's sins may deprive them of success, so they must both engage in sincere repentance so that Allah may grant them success.