I am adding another windows to a sunroom. This will go under the left corner window on the landing (see picture). So of course I will take out the left and right jack studs and cut the middle stud down. I'm wondering if I can get away with cutting only the first left and right king studs to make a stronger window header. For the windows on the right they use two 2x6's of the same length for the header. Can I leave the first 2x6 as it is and then put in a longer one below it to span the cut king studs?
I wouldn't mess with your kings. The biggest weakness in a wall of windows like this is stiffness. You want as much lumber going full-height as possible.
Also, that's not a header. It doesn't carry any load and merely offers window flange mounting and horizontal stiffness.
Pull the jacks, double the "header" (mullion, really) and toenail it in well, and carry on.