Of course, I kindly remind him to brush his teeth
One alternative would be to talk about his breath without going straight to the solution - I forget that myself and tend to go straight to solutions. After all, my solutions are fabulous! Why wouldn't anyone just want me to tell them what to .... oh, oops.
Part of supporting autonomy is giving our kids the space to think of some of those fabulous solutions on their own - the other part is then being willing to help them problem-solve if those "solutions" aren't exactly what they hoped. To use a montessori truism: "kids learn to make decisions by making decisions" and that includes less than successful decisions, so they can experience the whole process with our support backing them up, and helping them figure out the "what now"? parts.
So, again I remind him to please brush his teeth. Sometimes, this happens several times.
Try starting the conversation in a different place - hey, guy, your breath is pretty stinky in the morning, but toothbrushing seems to be a hassle for you... can we find a better solution? If he's not used to this kind of problem solving (if mom jumps to solutions, why should he be?) he might need some prompting. Can you set up the toothbrushing somewhere different? Can y'all look into mouth rinses for first thing in the morning? Gum? A tongue scraper? Maybe y'all could look into some of the causes of bad-breath together and find yet more possibilities - like a change of night-time snacks, or more humidity in the bedroom or a nasal rinse? There are dozens of possible solutions to morning breath and creating a healthier mouth environment.
I suppose I could give up on working with him
Sometimes a break is a valuable solution to explore. Its good to "red flag" situations where you seem to come up with only two options, though. That's often a good sign that you've gotten stuck in your thinking - and a good opportunity to go to your kids and say "hey, I can't figure this one out, lets put our heads together". And if that doesn't work, well, that's one of the things these boards are great for - seeing a bunch of different perspectives and possibilities.