It really isn't too difficult, all a matter of folding the right side in the right direction and pressing. I decided to write the tutorial on a wim. As I didn't plan on doing it, I took the pictures while sewing in the evening, ergo bad lighting. I tried to make the best out of them through editing, I hope you can see everything and I'll make myself clear. Please don't hesistent to ask anything you didn't get in the comments below.
First of all you'll need to modify the front piece of your pattern: just double the button placket! As you can see, on the original, 3 would fold under 4 to create a regular button panel, you'll need to add the width of the finished button panel by two, so in the end you've got four parts that form the panel.
For clarity sake, I numbered the parts of the button panel, so on the following pictures it'll be easier to follow what happens to which part.
The chiffon wasn't the best fabric to show it on as it's difficult do determine which side is which in the pictures, so I wrote that on each pic in a corner. It's crucial that you get that right, just take each step at a time to not get confused.
And that's it. Of cause you'll only do it to one front piece, the other with the buttons on get treated according to the pattern instructions- just like you would do it on a regular button panel.
I hope this is helpful.