Brake Fluid and brake "Adjustments"

It is not necessary to replace the brake fluid at this time, and doing so will not help the noise produced by your rear brakes.

Are you sure that the noise is coming from the rear and not the front? It is more likely that the front brakes will make noise if the discs accumulate some rust. In that case it might help to get the car up to speed - 50 mph or so, then shift to N and moderately brake to clean off the discs. Repeat a few times and see if that helps.

If the noise is really coming from the rear then it would be good to remove the rear drums and figure out where the noise is coming from. Good luck.

 

For my third gen, the Canadian schedule says to inspect brakes every 12 months or 16000 kilometers (10000 miles?). The Repair Manual is not really clear as to what constitutes an "inspection", or I've not dug deep enough. From my past Honda experience, brake inspection consists of:

1. Removal, cleaning and re-install of disc brake pads, and associated shims/clips. Check thickness of pads. Lightly lube all points of contact with anti-sieze compound.

2. Check (while the pads are off) that the caliper is moving freely on it's aligning pins.

3. Occasional check of disc run-out and thickness, with dial indicator and micrometer.

4. Drum brakes (not sure if second gen has them): you want to check thickness, and periodically (maybe every other check) loosen the hold-back clips on the shoes and refresh the lubed at contact points behind the shoes. You can do this carefully without removal. Just ensure you don't grease the shoes themselves. I used anti-sieze compound for this, not sure if it's kosher.

 

I agree with what Patrick said. Don't bother giving your heard-earned money to that dealer. The "flush" certainly won't solve your problem. (Clean and adjust may be appropriate, see below).
Now...the Chicago area is certainly in the "rust belt" . There's a possibility that your emergency brake cable is not releasing properly. If the car isn't driven regularly, rust may be the culprit. I would remove the rear wheels and drums (easy do-it-yourself), inspect, clean, lightly sand the drums and shoes. The 2009 has rear drum brakes. That will probably solve your problem.

 

I went in for an 80,000 mile oil change on my 04, they suggested new brake fluid and a clean and adjust for the rear brakes for $99.99 and $35.99 respectively. I figured since the car is 8 years old and I haven't ever changed the brake fluid, that sounds fair. I took it to the guy who works on my Corolla and he did it for $75 and $35 respectively. The maintenance guide doesn't discuss brake fluid, but I've never had a car that didn't say change at 2 years regardless of mileage...so I figured it seems reasonable.

 

Anymore estimates on a dealer flush?