Taking a monk archtype that replaces stunning fist as a bonus feat at first level (such as flowing monk) if I were to take the feat later after meeting the pre-requisites for it - would I still get uses per day as a monk or would it act like a non monk taking the feat?
You are still a monk, and the special rules for Stunning Fist are in the feat description, not the class description. If you take the feat at a later time using a feat, you still follow the improved use per day.