I stumbled on this picture on facebook this morning. It appears Kane was taking in a Bulls game a few weeks ago. And yes, that is his finger way up his nose. He wasn't picking it though, I'm sure he was just itching his brain.
If I knew anything about hockey I'm sure I could make some witty joke about penalty kills and boogers, but alas, I know nothing. It's a good thing nose-picking on its own is pretty funny.