I am not a pro here, so I would wait for one of the pro's to answer, however I did have a similar situation once with my ponderosa lemon tree.
I had a split once too. Since the poor thing was young and only had 3 limbs, I did not want to remove it, so I went out, and got some of that tree wound dressing ( looks like black tar) and painted that all over it, and then took that green stretchy plant tie instead of tape ( it is cheap and unlike tape, it is more breathable)and used that to hold it together. The limb eventually connected itself back together after a while and years later, it is a now a main large branch to my tree!

I am sure you could also remove it and try to root it also. You may have a 50/50 on that.

But like I said, this is just a personal experience, and you may want to wait for one of the pros here to chime in! Good luck! Christy

If you match up the cambium exactly and tape it tightly (with floral tape, not scotch tape) it may heal. If it's a jagged rip this may be difficult or impossible, but it may be worth a shot.

Citrus can grow a lot each season. So, if I were you, I would just cut off the broken branch and try to root it with some rooting hormone in a container filled with perlite as an experiment - if it succeeds, you got yourself another tree! The original Kumquat tree will replace the broken branch eventually.