Launch Dictation With Applescript
You can just simulate pressing fn twice:

delay 0.3 -- time to release modifier keys if for example the script is run with command-R
tell application "System Events"
    key code 63
    key code 63
end tell


Or from a terminal:

osascript -e 'tell app "System Events" to key code {63,63}'


The osascript command worked for me in Terminal but not in iTerm 2. The Start Dictation menu item also just plays the lower pitch sound without showing the popover in iTerm 2 though.