http://www.warrenborn.com/Unit.php?ID=FI080

Duke has a fist for his secondary attack type with brawling all through the dial. the damage value is zero the whole way.

Does that mean he can only do one click of damage? Why not just treat it like every other mech and use the primary damage?

Page 26 of AOD rule book
To make a close combat attack, a unit must be given a close combat order or an assault order. Close combat represents point-blank fighting between units.
Only infantry and ’Mechs can make close combat attacks. In order to make a close combat attack against a target, the attacker’s front arc must be in base contact with the target. A ’Mech with the speed mode can make a close combat attack against a target if any part of its base is in base contact with the target. A close combat attack uses neither the nor range types; it uses either no range type or the range type.

Fortunately for you, that's an easy question to answer. As you said, the secondary close combat attack has brawling. So what does the SEC say about brawling? And I quote:

BRAWLING (optional) This unit gets +1 to its damage value when making a close combat or special attack against opposing figures, regardless of the damage value used to resolve the attack

So it goes without saying that you'll use the primary damage value when performing close combat or special attacks with this 'Mech. When on its first click, "Duke" Nova Cat is capable of doing 6 clicks of close combat damage or 7 clicks of damage when charging.

See? You'll get answers to all sorts of question here.

Melee for Secondary rarely is used as most will use the Primary Damage in Close Combat.
Like Nanhold says, the damage output is quite often low if Melee is the Secondary damage type. It saves points and then the slot is used to have hold other effects like Agility, Hand to Hand, or Brawling.

Enjoy playing with the Duke ;) Otherwise keep your RotS forces away for him if you're playing agianst him.

I always liked using retractable blade too, im either gonna shoot you for 10 or punch you for 7 its nasty.