...I do note that the Wiki article mentions that all members of the Department are Flowers (that being the Security Dandelions and such) but what is the actual recruitment process (if any) for the Department?

I would assume that trusted and extremely competent agents might have a chance at fitting into DES' ranks since they would form the vanguard of Headquarters itself but without prior cases, I'm not sure if this would be too canon-breaking for the DES.