Where must you send your application form of illuminati after filling it?

Perhaps St. Elizabeths Hospital, East Campus, Washington DC.

Seriously though, the Illuminati has not existed since the late 1700's, and even that short lived organization did little more than seek knowledge. Were you alive then, you likely would only have had to ask to join. If you have an actual application form, be wary of any "membership fees" as such is likely some form of scam that preys on the gullible.