Firstly you'll need to figure out the colour codes on the existing pickups. Do you know the manufacturer?
Secondly I imagine you´re aware you are replacing a single coil with a humbucker. That wiring scheme is versatile, but designed to make the most of three singles.
You´ll need to decide if you want to wire them full humbucker all the time or if you want to be able to split them at some point.
Bear in mind if you don´t split them some positions in that scheme would end up with 3 or 4 coils all in series / parallel at the same time which may end up really loud/quiet, or at least not very well balanced betwen positions.
Personally I´d be inclined to simplify things as much as possible by sticking with single coils, at least for the neck and middle if you haven´t already bought them - maybe even the existing ones if you like them.
Once you've that sorted out and assuming you don't require any splitting it should be a case of splicing the JB jr wires to the equivalent colour in the existing wiring's colour code, and white and red just spliced to each other as in your own diagram.
If splitting and you are going with neck and middle humbuckers too - you´ve mentioned you´ll replace them, but not what you´ll replace them with - you´ll need to decide between splitting individually (which would need an additional switch per pickup) or splitting all with a single switch. I think that´s possible but I´m not even 100% certain, I think it depends on the type of switch.
A single switch would mean you couldn´t have one pickup split and another full HB.
(If you are going to split the JB jr, the simplest way would be to add a switch or push-pull pot to connect the red & white to ground.)