I don't recall anything in the text to indicate how old Denny might be. As a Subaltern (a "Mister") he is either an Ensign or a Lieutenant. I'm inclined to think the former, as he's never refered to as Lieutenant. (That is, not pointing out he's in the lowest position.) I don't have specific regulations for the UK militia at that time, but an Ensign in the Regular Army could be as young as sixteen years of age.

Now, rank in the Militia was dependant upon income derived from property (unless special consideration was made, as in the case of Henry Austen), and the regulations might be laxer than in the Regulars. The lack of income might also keep a Militia Officer at a lower rank.

Either way, if one were to think of Denny as a 16 or 17 year old, it becomes quite easy to see how he could fall under the thrall of a Wickham. He's reaction once "caught" also seems to reflect that of a less mature person.