If they flush it or if they drain it they will need to burp it. As others have mentioned it sounds like your dealer is trying to flush some cash out of your wallet. I’d tell them to drain it and burp the air out of the system.
I did my timing belt and water pump on my 2010 Ridgeline. I just added coolant and let it run with radiator cap off and it works the air out itself. You'd think by now dealerships would stop trying to rip people off.
If they haven’t started the work yet I’d tell them that you expected all required work to be included in their estimate and that they should include that in their initial price. If not you’re happy to take it to a wonderful independent shop.
Basically turn the tables on them where they either do the flush included or lose all your business.
The factory service manuals detail a 24-steps "for dummies" process just for the "refilling" part of a cooling system service. The steps involve having heat on and then off and then on, listening for air-bubble noises, running the engine, and verifying between steps that you are maintaining sufficient fluid level in the reservoir and radiator. It's intended to make sure there are no air pockets anywhere in the engine or the rest of the system. There's very particular and specific info on making sure the heat exchanger for the rear seat floor heating is absolutely bubble-free. It didn't take long to get all the bubble-burping done on mine. Just know it isn't quite a "pour some in and drive away" procedure when you follow all the workshop manual steps.
One of the hot-rod shows on TV recently showed a vacuum-fill method for making sure there are no air pockets. In a nutshell you get to pull a serious vacuum on the system, extracting all the air. The bigger hoses collapse under vacuum, and your pump keeps drawing air out until none is left inside. The liquid coolant is allowed to be sucked in until the system is again full of just liquid. I have a few cars that have issues with getting air bubbles out, and this may turn into a go-to if I can easily make the radiator-cap fitting with a three-port valve.