Weather proof connection from FMC to box
In my opinion FMC is no good for this application, even though it's only barely outside, it's not rated for outdoor use.  (I realize lots of people would either disagree or figure it's close enough and run with an indoor rated wiring method.)  

The easiest thing to do would probably be to set a box inside and transition from FMC to UF cable - run the UF through the wall to the back of the box with a suitable waterproof connector such as this one from Arlington: 

http://www.aifittings.com/catalog/non-metallic-cable-fittings-and-supports/uf-connectors/UF50   



To connect the UF connector to the inside box, you could use an indoor-rated clamp as long as it's listing / instructions / labelling says it's for use with UF.  It might be easier to just use the outdoor connection indoors as well.  

You might be able to find what's called a "transition fitting" or a "this-to-that" that will connect UF directly to FMC but again it's probably simpler and easier to just transition in a box.