He is not doing it for me. At all:
(Is it just me, btdubs, or does Sam Claflin look a bit like David Tennant? Not that that's a bad thing AT ALL in general, but as Finnick, it doesn't work.)
There's one more picture up at MTV, that suggests to me that the casting might be more about the charisma than the look, so click on through if you're interested.