There's not a Valencia's coat of arms because it isn't an spanish last name. Nobody in Spain has such last name. This name surges when spanish come to America without last name (most of them; originally all this people call themselves Hernández, Rodriguez, Pérez, etc. that in fact just tell us who is your father: Hernán, Rodrigo or Pedro )and when they get register tell their city of origin... in this case Valencia, Spain.
Other examples of last names that there aren't in Spain are Palencia, Madrid, Valladolid, etc.