Document, document, document. If he asks you to do something or you ask him to do something, put it in writing (even after the fact). You can easily spin this to be in the name of collaboration - "Let's use a ticketing system to keep track of our tasks while we're working together, so it's easy to keep each other updated asynchronously." While you're in a meeting without access to your computer, try to take notes and verify with him in the meeting that they are accurate - "OK, I'm going to do A and B and you'll do C and D, and we'll report our progress tomorrow, right?"
It's not clear if he's told you that he doesn't want you to interfere with his chances of promotion, or if that's your interpretation of his behavior. If it's the latter, keep in mind that it's your interpretation and try to give him the benefit of the doubt. If you do still think he feels threatened, you can try to highlight the differences in your skillsets when divvying work, and let him take the lead in meetings on your joint projects with management and stakeholders. Basically, show him that you aren't trying to take the rung he wants.
At the end of the day, there are some people that are so entrenched in the rat race they don't realize not everyone else is, and really think that all of their peers are trying to climb over them. Protecting yourself by keeping a written record of what everyone agrees to do and executing on your tasks is how you keep moving forward - if your coworker tries to play games you can nip it in the bud quickly, and if he doesn't you all look like good, organized team players.