Unless I'm missing something, why won't the simpler MAX()
function do the job?

Example:

row ... AC ................. AG
1100 .. 5/5/05 2:00:00 PM .. 2,500
..
1824 .. 5/7/05 3:15:00 PM .. 1,700

and in any open cell, "enter" the formula
=MAX(AG1100:AG1200)

where "enter" means type "=MAX(", and then click
the cell of col AG (the flow) in the row
corresponding to the begin date, and drag to the row
of the end  date.

Granted, 724 rows is a bit of dragging, but how often
do you plan to do this?

If this is something you routinely plan to do, then
you could dedicate 3 cells, eg:
A1 = begin date
A2 = end date
A3 = max flow

where 1 and 2 are manually entered, and

where 3 contains a formula (perhaps one similar to what
Pascal is working on) -- or --

where 3 is simply populated when a button is pushed.
The button would trigger a sub that would use
the dates  contained in A1 and A2, then do a "maxflow search"
in col AG between (and including) the rows delimited by the 2 dates.