No, catching the flu from Fido isn’t possible. Even though the influenza virus does exist in dogs as well as cats, the viruses these animals get are completely different than the viruses that affect people -- and they can't be passed to human beings.
However, dogs and cats can definitely carry human cold viruses, which they can then pass to children and adults. So if your dog has the symptoms of a cold, it's even more important for family members to practice good hygiene and wash hands thoroughly after close contact with it. Dogs can also harbor the strep virus -- so if your child is getting repeated strep infections, you should have your dog tested to see if it's a carrier so it can be treated as well.
Keep in mind that certain coughs and colds can be rather devastating to pets. It's a good idea to call your vet if your animal appears to be sick.
