Can I, or my dogs or cats contract bird flu from my pet birds?

Avian Influenza South Africa 2017
The information provided here is not an official statement but is meant to provide some general information on bird flu because of the break out of bird flu in September 2017 in South Africa.
Bird flu or Avian Influenza (AI) is a family of influenza viruses that mainly affect birds. They are named according to two proteins on the surface of the virus (Haemagglutinin and Neuraminidase). The only ones of commercial concern are the H1, H5 and H7 types. There are dangerous (HP or highly pathogenic) and LP (low pathogen) strains. So when you see someone talking about HPAI H5N8 that means the dangerous type of H5N8 avian influenza.