Unfortunately, vigorously brushing your teeth won't solve the problem of bad breath in ketosis. That's because it's not about the mouth, it's about the ketones that are passed from the lungs into the air you're breathing out.
When you are in ketosis, especially in the early phases of it, you're almost certain to have an odor to your breath. You can add fresh mint and/or lemon to your water to freshen your breath. Your coach may have other suggestions.