I kinda doubt he’s going to disclose the gerbers and BOM for the diagnostic card, and that wouldn’t really help you much in designing your own anyway. I can help you design your own using the same techniques I used to design the NTAG I2C Plus test card on the store, though.
A great place to start would be the Inductance Calculator I posted. Once you have that working you’ll need to find an NFC chip or an LED that you want to put on the card and find it’s “input capacitance”. Then you can use an LC resonant tank circuit calculator like this one to calculate what Inductance your trace antenna will need to have in order to resonate at 13.56MHz with that input capacitance. Then you can use the Inductance calculator to calculate a coil dimension that results in the Inductance you need (guessing and checking until it matches). Then you can lay everything out on a PCB, and put an extra capacitor footprint in parallel with your NFC chip or LED in order to tune it later (in case your antenna Inductance is a bit off). Then you should be good.