Would it be wrong to send my ex's best friend a gift?
Why are you sending your ex's best friend a gift?
Because I want to get on his good side and get back with my ex-girlfriend.
It's wrong to use your ex's friend to get to your ex. That's not a good thing to do.
I need to make her jealous.
If you don't actually care about her best friend, then using him to get close to her is just going to end up hurting him and then she won't want you back. There are better ways to try re-entering a relationship with an old girlfriend.