Despite a dodgy serology test...

..not my interpretation, tweet from WHO's Gregory Hartl, it seems that at least one son of this outbreak's first reported H7N9 case (Case #1, 87M) has been confirmed as also being H7N9 positive. 

What does this mean? 

It doesn't mean the sky is falling - contacts, by their very nature share things. In a family you often share (inhale, have land in your eyes etc) aerosolized (virus-laden) droplets as well as common surfaces contaminated by with those aerosols, when you have an acute virus infection. 

Coughing and sneezing do that. But you also share common tasks. There is so far no clear evidence of direct Dad to Son (or Son to Dad) transmission here (there is a timing issue that is intriguing)- the father and son may have simply shared the same airspace (I think its pretty safe to say this is transmitted through the air in some form) with an animal host during contact, handling, butchery, cleaning etc. 

Despite testing of animals to date finding very few have detectable H7N9 infections.