“Typical” is more common but “a typical “ could be used, but it would have a different meaning. Also, in speech you would have to be careful not to sound like “atypical” which has the opposite meaning. In typical fashion he ... (This is what he would be expected to do. You could even say “in his typical fashion, he ...” to emphasize that what was typical for him personally might not be typical for others) In a typical fashion he (rare. For example, if it was known that people of different nationalities behave differently, using “a typical fashion” would emphasize that there were several fashions, and he was behaving according to one of them.)

"In typical fashion" reads correctly. Inserting "a" or "the" would make it sound unnatural to the English ear. You don't always need the article in constructions like this. For instance: With complete sincerity, he explained the situation.

No It Shouldn't Be