FlashFXP has an undocumented feature that allows just this
Added program execution after transfer complete.
To use this functionality you must add the following section to the FlashFXP.ini
[run]
app=<full\path\to\exe>
param=<any params you need to pass, use the %f macro to pass the filename>
show=1
show application window has two values 0=hidden 1=visible
Simple Example
[run]
app="c:\vscan.exe"
param="/scan %f"
show=0
The sounds dialogue will also let you choose a batch file instead of a sound file to execute on the completion of your chosen event.
I will try to remember to add this to the advanced section of the help file on the next release.