Yes, dogs can get the flu, just as humans can. There is a Canine influenza virus that was recognized in 2004. The flu virus is very contagious and about 80% of dogs will get symptoms such as a runny nose, cough, sneeze, lethargy and fever. 20% of exposed dogs may not have any symptoms. The fatality rate is very low in otherwise healthy individuals. Most of the outbreaks are in shelters and kennels where dogs are confined under stressful conditions and exposed to many other dogs. The average house dog is at very low risk of even contracting the virus.
Should you vaccinate your dog against the flu? The majority of flu cases in dogs will heal uneventfully, just as you and I do, in about 2 weeks. There will be a few that progress to a more serious pneumonia that can become life-threatening. The thing about vaccines is that they are not benign. Vaccines can cause a number of side-effects and weaken the immune system rendering it ineffective to manage future disease exposures. A healthy dog that goes through a disease exposure and recovery will build strength in its immune system and be better able to fight disease in the future.
It really is ok for your pet to get sick. It is a part of life and will help your pet gain strength.