Dogs have belly buttons, they’re just flat!
The fact is that all mammals that gestate (develop prenatally) inside a placenta have an umbilicus — and that includes dogs. Yours has one too or he’s an alien dog sent by an advanced intergalactic civilization to live among us and observe us. Assuming he’s not terribly Chewbacca-like and that you can get him to cooperate, you should be able to see a little oval-shaped indentation on the abdominal midline, about halfway between the sternum and the genitals.
Dogs’ belly buttons don’t create big lint-trapping depressions like people’s do, and it’s a good thing since it’s likely that they would get pretty gnarly and require routine maintenance. In people, the “floor” of the belly button is referred to as the umbilical tip, and if it protrudes past the opening to the umbilicus, you’ve got yourself an outie.