Hey, Sean. Nice call on the Kinks' influence. It's definitely in there.
Fujindemon has it right. There are three albums and scads of singles and bootlegs out there (check on eBay), the latter of which are now pretty pricey as their cult following expands and demand increases.
They're the real deal. Their live shows are terrifically intense--did anyone catch them on Letterman last week? That was only a small taste of what they deliver live. Not only does their blend of old-school blues with both "classic" and indie/garage rock (on any given night, their covers might include songs by Son House and the Kinks, or Bob Dylan and Iggy Pop)enable them to stake out their own sound, Jack White actually writes good songs. They not only have a sound, they have content, and in due time, they'll transcend the hype and outgrow their cult following and all those "hipster indie rock critics."
If you get a chance to see them live, don't miss it. And pick up those albums, the last two especially. In fact, that whole Detroit scene is pretty cool.