Colleague doesn't work on any task unless request specifically comes from the boss

I don't want to involve the boss every single time.

What should I do?

You should talk to your boss and ask how often he wants to be involved.

You should also clarify with your boss what your working relationship should be with your colleague and if you should directing his actions or not and the relative priority for closing tickets versus making the product better.

It seems clear that you and your colleague don't have the same views regarding your authority and his responsibility. Clarify that.

I think your colleague is acting very sensibly.

1. In a flat hierarchy, why do you keep asking your colleague to open tickets? Why aren't you doing it yourself? But also what you are describing sounds very much like scope creep. If people keep creating endless tickets, nothing will ever be finished. New feature requests really need to be discussed to decide whether they need to go in, or are "nice to have" ideas for a future release.
2. That sounds like the colleague is following the process. The boss allocates tickets, not you. Your colleague wants to be seen to be productive by working through the tickets allocated to him, not new ones you have decided to offload onto him.

Your actions should be aligned with what the company wants, not some lofty goal of making the product "better".