1.
When Ron left in Deathly Hallows while they were on the run, Hermione left too. They may or may not become friends again. Harry meets Reddington and while he doesn't agree with his methods, understands his reasons. Obviously Grey!Harry.
2.
Reddington saves Harry from the Dursleys and adopts Harry. Harry gets raised by Red but still attends Hogwarts.
3.
Harry gets betrayed by the Weasleys (except the twins) and either runs into Reddington, or gets introduced to him after something happens.
After 1,2 or 3 happens
Later when Reddington works with the task force, they need help with one of the cases. So Red calls Harry. Harry now being part of the Aurors/Unspeakables/ some secret and awesome organisation, comes to help. Cooper knows about Magic (high up government) or not (kept from him on purpose by corruption people).
The task force learns about magic and get introduced to the wizard in world. They might go into magical places for resources or leads or something. Harry might consider staying on the task force, because he's got nothing left in England or is bored.
If 2
The team find out Reddington has an adopted son that no one knew about, who is also magical, and that Red is a good father.