I'm going to make my boyfriend stop a snapchat streak with his ex
Why do you want him to stop the streak?
He should be spending time with me, not flirting with his ex.
It's understandable that you want your boyfriend to give you more attention than someone he has no relationship with. You should try to fix the relationship because he's already looking at other options.
So I shouldn't remind him that I exist?
Yes, you should. If he sill refuses o give you the attention you deserve, then consider leaving him.