it doesn't matter which direction.. a matter of fact, it's actually best to flush it one way, and then reverse flush it the other.. a few times.. flush it until it comes out clear.. use a solvent if you like, if you don't, you'll just find it takes longer..
acid? really? dude.. that wasn't done on good advice.. seriously.. it will NOT eat rubber, (so long as it isn't REAL rubber, which most hoses aren't)- it will eat ANYTHING found on the periodic table or organic, it may take more time with some stuff than others, but not something synthetic.. but still... acid? by the way- Aluminum, iron, copper, bronze- all found on the periodic table.. steel is a combo of several periodic table critters... so, that was brave.. If that stuff wasn't flushed before you reattached the lines to the pump, and your engine got a wiff of it- I bet your freeze plugs aren't long for this world either.. especially if they are copper or bronze- which reacts to acid a lot faster than steel or aluminum..
CLR is good stuff.. just make sure you get it all out.. flush it until you'd feed your dog the water with confidence!
the T fitting mentioned is a nice gadget.. It isn't expensive.. grab one at the parts store..