Don't know as a engine flush but years ago when I had my K5 Blazer, every time I did oil/filter change, I'd drain the tranny ATF then refill to keep it fresh. Off road duty a lot back then.
Anyway, I always took the used ATF and bottled it. Carried a bottle and every time I filled the gas tank, I added a dose of the used ATF with the gas fill. Just a way I got rid of the ATF.
Never had any problems doing this. Just if I used a bit more tank after tank, my plugs sometime would actually get a little bit of a red'ish tone color on the plugs insulators.