Peri: See if this makes sense.
Create a Smart Campaign. Add filter "FILLED OUT FORM" to the Smart List. Identify form and/or page.
If you know the lead source, under Flow, select, CHANGE DATA VALUE. Attribute=Lead Source. New Value=xxxxxxxx.
Under schedule, click RUN ONCE.
Once you've ran it, go back and replace the filter with a trigger (FILLS OUT FORM) to catch leads going forward. Also, delete the FLOW since your form will now be capturing Lead Source.