If the fluid isn't a pink or red, I'd just recommend changing it by dropping the pan. This way, about 1/3rd of the fluid is new, and can begin to gently clean what the old fluid couldn't, and have much less risk ruining something.
Honestly, you can "flush" your fluid yourself, just disconnect one of the cooling lines, stick a rubber hose on the end and put it in a bucket, then start the car, let it run in park until you see air bubbles, shut it off, add 4 quarts, and rinse and repeat until the fluid is pink again. Usually takes 3-4 cycles.
Now all the fluid is fresh, and you're good to go. I would still recommend replacing the filter. To make it easy, the last time you pump out the fluid, drop the pan before you add the last 3-4 quarts. The pan will be nearly empty, and it'll be a lot less messier. Change the filter, clean the magnet, wipe the pan out, and replace the gasket, re-tighten, and then add the last 4 quarts.