WKKW put together a guide for downloading the KK App outside of Japan:
http://www.welcometokodakumiworld.com/howto/KKapp101
Honestly though, it's not really worth paying for and using at this time if you can't read Japanese. That might change as it rolls out more though.
As an aside, I e-mailed Koda Gumi asking how international fans were supposed to use the app if they couldn't download it, considering the e-mail from them said the international fanclub would be replaced with it. Typically, they were incredibly unhelpful and basically resent the announcement email and then said to contact KK App directly if I had any questions about them. So I sent another e-mail via the site...we'll see if they are any more helpful, but I'm not expecting it.
It does really seem like international fans are being left behind with this one. I'm surprised they'd shut it down while she's on a tour that offered tickets for international fanclub members.