Can a swollen leg get so swollen it starts to split the skin?

Yes. This is common with venous insufficiency in which patients develop venous stasis ulcerations or "holes in the skin". The problem is the valves in the veins aren't functioning properly and blood that should return to the heart stays in the lower extremity. The build up of fluid causes the skin to breakdown and open up.
Absolutely. It is entirely possible. If you have chronically swollen legs, it is important to get the swelling down as effectively as possible. When severe chronic swelling occurs, meticulous skin care is essential to make sure your skin doesn't split and that you don't get an infection.
Swollen leg. the short answer is yes the question is why is the leg swollen you need to get evaluated sooner rather than later because as the swelling is not under control the issue of the skin splitting will continue to worsen.
Yes. Yes, a leg can become so swollen that it can cause a splitting of the skin. The hope would be that the underlying cause of the swelling would be diagnosed and successfully treated before this occurs as splitting of the skin can cause increased risk of infection among other potential problems.