The easiest way to connect to your Xbox is via your controller with a Y adapter, aka a TRRS/CTIA (tip-ring-ring-sleeve) adapter - the type that lets you plug/combine a mic and headphones into a single 3.5/2.5mm jack. The plug of the adapter should look like the bottom image in the photo below. Make sure the Y adapter has ports labeled specifically for your headphones and your mic.
Note you cannot use a USB Sound Card to connect the ModMic Uni or Kimura to a USB port on your Xbox.
Microsoft requires a physical security chip (called a security key) for USB audio. The fees for this chip are so high that an Xbox-compatible USB product is not likely in the near future, as we'd have to create a specific Xbox product separate from our existing lineup (and charge more for it).