Is a VFR flight following request implied when talking to tower and advising them of your intended airport?
It is not. You must explicitly add 


  Requesting VFR Flight Following 


Depending on the airport in question the tower may simply tell you to contact approach once in the air to request flight following. Other towers may set it up for you. 

The notation of your destination is extraneous. When departing you generally tell the tower you direction of departure not your destination. 

Flight flowing is also not an implied bravo clearance, you will need to request that once in the air. If you are taking off from a towered field you can ask for a handoff when requesting your clearance, this may help facilitate your clearance request as well as your flight following request.