in general i think flushing is the whole thing, including the Epsom Salts if youre doing a flush that uses them. it would be nice if a really experienced flusher answered here, as i've never had to do a second flush due to a stuck stone. but it seems like it would indeed include the epsoms, esp. if a stone is stuck.
and as to whether its safe to do a flush so soon after doing a previous one, in general the answer is its best not to do it. but if there's a stone that is really stuck, what's the alternative? its much better to do another flush than to end up in the hospital like capco did recently, using a mechanical arm to get stones out of his bile duct (capco, sorry if i'm mis-stating your experience). and once you get to the hospital, a doctor then would say, "just look at what the flushing did, why don't we just roll you into surgery right now!") so i think if it really is a stuck stone that is big enough to stop up the works so to say, yes, flush again.
i do think when people get a 'stuck stone' its really that a big stone got stuck, or, that there's a stone stuck in a new more dangerous place. that stone that's blocking up the works was stuck in a different place, before the flush. (knowing that doesn't mean that it doesn't have to get taken care of, of course it does...)