That is true, dogs are often associated with loyalty, love, and bonds. Let's say that your old dog in your dream represents, perhaps, your past friendships? Or maybe even you from the past? Fleas in dreams often represent conflict, anger, retaliation, etc. Something that would get in the way of someones loyalty or people's friendships. Perhaps this is a warning that a friend you've known for a long time might become upset with you or you'll become upset with them? Though, it could also be a warning that an old friendship has changed in a negative way or even that you've changed in a negative way.

This may not be completely accurate, but it's something to definitely consider.

Edit : Ah! I just had a thought! Since you're removing the fleas from the dog; maybe you're removing the bad aspects of the situation? Perhaps resolving whatever issue it was? Maybe it's saying what could have happened if the situation had continued. I remember you made a post about how you wanted to make others happy and that you really pushed yourself and pretended to be something you weren't a lot of the time just to make others proud. Dishonesty is the opposite of loyalty, even if it has good intentions. I remember you said that you would work on it. Maybe this is sort of like an aftermath dream? Saying that you're improving?