I had an idea for creating a magic item exclusive to dragonborn, the idea is this:

Gauntlets of Draconic Ancestry

Wondrous Item, Rare (Requires attunement from a Dragonborn, must be proficient in unarmed strike)

The gauntlets appear to be made of the scales of various dragons. When attuned to them, the gauntlets change to the color of the dragonborn, as well if the dragonborn uses the command word, they may expend their breath weapon on the gauntlets and use the same level of damage for the unarmed strike on top of the unarmed strike damage (I.E a silver dragonborn monk at level 3 would have 2d6 of cold damage along with the 1d4 per strike). The bonus damage lasts for 1 hour and can be used again the next day.

I would like to know how to improve the weapon so that it is more balanced. Any criticism and recommendations are appreciated.

Well, first of all, everyone is proficient with unarmed strikes. 

For balance, compare to the flame tongue and frost brand.  I think rare is about right. 

Your formatting could use a bit of work, though. 

Gauntlets of Draconic Ancestry

Wondrous item, rare (requires attunement by a dragonborn)

These gauntlets appear to be made of the scales of various dragons.  When you attune to them, the gauntlets change color to match your scales. 

As an action, you can speak the command word and expend one use of your Breath Weapon trait to charge the gauntlets with the destructive energy of your breath weapon.  For the next hour, whenever you hit with an unarmed strike, the target takes additional damage equal to your breath weapon damage.  The damage is of the damage type associated with your draconic ancestry.  The effect ends early if you die.  Once you have used this ability, you cannot do so again until you finish a long rest. 

You might want to make it very rare.  Then again, it's limited enough that you might not. 

Thank you for the help, it is much appreciated.