If an SS Boxer is pairs with a flashy Ssw, puppies have a 50% chance of holding markings. If 2 flashy Boxers (Ssw) are bred together, the resulting litter will be puppies with markings, unless genes skip a generation to bring in the white coloring.
When people talk of a fawn or brindle Boxer, they are usually actually talking about a fawn or brindle Boxer with white markings and a black mask. While this is a common color combination, it is not the only combination for this breed.
Therefore, if your Boxer is just fawn or brindle, he does not need to have any of the white markings.
He would just be considered to be fawn or brindle Boxer.
Puppies often change in color and markings as they grow. However, if a Boxer puppy was a fawn or brindle without any white, that dog would be registered with the AKC as a Fawn or Brindle and the Markings Section would not be checked off.