I think the question is fine but awkwardly formed.
He's asking something like the following:
Say we had a list of all possible flops, numbered from 1 to N. Given 2 known hands, we can find the (showdown) equity for flop 1, for flop 2, 3, 4 ... N. If we average these we get what he's asking for - the average equity on the flop.
Now - OP. You know what the average equity on the river is going to be - that's literally what showdown equity IS. And you know what your preflop equity is.
What reason do you have to believe that the average equity on the flop will be different than the river or preflop?
A more interesting question might be... how often will we be ahead or behind? And by how much? I wondered this too so I wrote a little article about it years ago.
http://rustybrooks.com/poker/new_analysis/
Granted, it's about the game razz, but the idea is the same. It is your hand vs a range, and it makes a plot of the potential equity outcomes on the next dealt street.