The first thing you need to do is talk to the player again. Explain, in neutral and non-accusatory terms, why his use of the phone is frustrating to you as the GM. Have examples ready, in case he says it's not affecting anyone - for example, "When your turn comes up, I have to spend time reminding you of what's going on, even though everyone else already knows. That slows the game down for everyone and makes it harder for the other players to get things done."
Then ask him why he feels he needs to be constantly using his phone. He may have a good reason - for example, one of the players in my last campaign was sometimes on call on game days, and was required to respond immediately to messages. Or your player might be dealing with a serious personal issue that requires constant attention. If that's the case, discuss ways to work around the issue: for example, can the game be moved to a different day, where he won't need to be on the phone as much?
If he doesn't have a legitimate need to be on the phone, he may express this in ways like, "Look, it's no big deal, I'm paying attention, okay?" or "I'm only doing it when it's not my turn, it's fine." If so, then you need to see if the issue is actually that he's bored at the table. (He may not want to say this outright, since you're friends and it's not considered "nice" to tell your friend that you're bored with their game.) If he's bored or feels like there's nothing for him to do, then this is something you can address as the GM. Find ways to involve him more, so that he doesn't get bored enough to turn to his phone. (But be careful not to leave out your other players!) Ask him which parts he finds boring - maybe he lives for combat, and hates the role-playing bits. Or maybe combat is just dice to him, and he prefers to be up to his ears in intrigue. Whatever it is, work with him to get him engaged enough in the game that he doesn't need to turn to his phone for stimulation.
If he's bored at the table and doesn't want to be more involved, you may simply have a player who's there because friendship, not because he actually wants to play. If that's the case, it's better for both of you to let him walk. You say you don't want to sour your friendship by booting him, but if this keeps going on, your friendship is going to sour anyway as you get more and more irritated by him and he gets more and more frustrated. So tell him that you're glad he gave your game a shot, but that since he doesn't enjoy it enough to truly participate, it would be better for both of you if you found some other activity to do together.
tl;dr: See if the player has a legitimate reason to be on his phone, or if he's just bored and needs more involvement in the game. But if neither of those work, be prepared to let him walk for the sake of your friendship.