Peter, probably the quickest way to do this would be to actually put the download code inside the loop... but make sure you create some sort of incrementing system.
Like set a variable such as: $incnumber = 0
then inside the loop have it increment like: ++$incnumber
then attach the variable to both the name of your download button and your looped download code, so it would look like this:
WA_DFP_DownloadFile("WA_DownloadResult1", "uploads", "".$row_WADAloadingDock['fileName'] ."", "[FileName]", false, false, false, "", "", "", "");
<input type="submit" name="download<?php echo $incnumber; ?>" id="download<?php echo $incnumber; ?>" value="Download" />
That way, the file name will populate correctly in the loop and download behavior knows which one to trigger based on the dynamically created unique number you added to each one.