Yeah, lots of ways to do this. And I need to get my ass outside and do some of it!
Most "recipes" for using baking soda+vinegar call for putting baking soda on the thing/at the place where you want grease gone. Add "just enough" vinegar to turn the baking soda into a thick soupy paste. OR do this in a seperate container you can mix first, then spread/pour/brush or otherwise dispense the soup onto the greasy surface. Maybe this is a 50/50 mix, maybe not. Then add boiling water to help clean/activate/rinse.
Now, how you do that for a grate I can't say. But in order to minimize the amount of fluid needed to reach both sides of the grate I'd suggest lying the grate down on a large black trash bag so that the natural "pockets" formed by the bag help retain and surround the grate rows.
If, after brushing and rinsing, that didn't work put the grate into the bag with a relatively small amount of ammonia and close the bag tightly. Leave it for a few hours. The baked on grease should wipe off more easily and then just rinse away the ammonia. Try to not kill too many brain cells sniffing the ammonia; it can knock you on your ass out cold if you're not careful.
For baked-on grease streaks on the outside of the kettle try soaking a paper towel or rag in ammonia and place it over the grease spot. "Kevin" of Weber shows using Windex (not the Weber product LOL) in one of their videos to clean the outside. Same idea but less concentrated of course.