If you can't get to it I would avoid flushing. I would stick with the coatings which contain and stop rust. I sprayed something like that from Eastwood inside my channels. I have heard several storied of solvents coming out later and ruining paint jobs as well as clean areas disintegrating from the inside out.
If you can't get to it, I would not flush it, just coat it with a rust neutralizer coating. That's just my opinion.
And oh, the Eastwood spray bottle for spraying the inside channels was a disaster. That black Sh** wouldn't come off the face, hair, arms or whatnot for a couple days!