To cook chorizo in a skillet it takes around 5 minutes but you may want to cook it a bit longer if you want it cooked more.
The chorizo comes in two different forms which is the sausage link form and the ground form and if it's the sausage form of chorizo then you just need to turn the sausage over and cook the chorizo for 5 minutes.
You could also chop up the chorizo to make sure it's cooked fully.
If it's the ground chorizo then you stir it in the skillet in some cooking oil and when it becomes brown and steamy then it's fully cooked.
Either way both types of chorizo takes around 5 to 7 minutes at most to cook the chorizo fully.