There are a number of illnesses that can be passed between humans and different species.
Chickens cannot catch the common cold. In most cases they do not get the forms of flu humans get. However flu viruses are very adaptable. The current swine flu is a mix of swine, avian and human strains, and that has been known since early on. H1N1 refers to specific characteristics of the strain; adding an A in front makes no sense whatsoever if the A refers to avian. If it refers to flu type A then it does make some sense as the seasonal flu is type B. From wikipedia "The hemagglutinin (H) and neuraminidase (N) proteins are targets for antiviral drugs.[23] These proteins are also recognised by antibodies, i.e. they are antigens.[11] The responses of antibodies to these proteins are used to classify the different serotypes of influenza A viruses, hence the H and N in H5N1." There are at least 16 different H subtypes and at least 9 different N subtypes.