Obviously the actual battling will need a ton of reshaping and retooling to get working on tablets, let alone phones, but I feel like buying items, equipping heroes, and entering leagues could be successfully performed fairly harmlessly on a small screen.
It's in the works, but it will be a standalone game. http://forums.cardhunter.com/threads/loot-and-legends.6270/
I use Photon, it does the job, though it can be laggy and isn't recommended for MP. Seeing as Photon is able to do it, controls shouldn't be too difficult to handle.
Given the fact that Loot & Legends is being shut down, I think the idea of a mobile app, possibly one that includes battle as well, is worth revisiting. Given the effort of writing a mobile app from scratch, it might be even smarter to port the game from Flash to HTML5. This would free Card Hunter from the legacy of Flash, which is no longer supported by Adobe, as well as allow for play in a wider array of browsers and platforms. Mobile support would become a matter of an HTML5 compatible browser. This would also restore Linux support. Of course the reality is more complicated than that, but the clock is ticking on Flash.