Apparently, there are conflicting answers to your question. Here's something I found relating to it...
Happy Dog Land: Can My Dog Get Swine Flu?
...which states that dogs do not appear to be at risk.
But then, I found this...
Can Dogs Catch Swine Flu?
...which says that, in a short answer, yes, your dog could catch it.
There is also a very nasty canine flu going around. Here's a CDC link about it..
CDC - Influenza (Flu) | Canine Influenza (Dog Flu) Q& A