When I say it goes ACROSS the inductive device that means between the + and - terminals of the device , NOT between Vcc and GND.
I don't know where you got that from because it was certainly not any of the links I posted because all of the devices in all the links I posted were switched on by something , like a transistor , (although an on/off switch would work as well) so the diode was always across the coil of the relay or solenoid or across a motor but NEVER across Vcc and GND.
Go back and look at the schematics. The diode has to go across the inductive element, be it a relay, a solenoid , or a motor. I have heard the one exception is electromagnets but I don't know why.
In the ZIP file there is a document named "Sainsmart UNO Starter Kits Tutorial.PDF"
Open this PDF file and scroll down to page 80, figure 19.2
If you look at this schematic you will see that there is already a diode in place on the relay board. The schematic is difficult to read because of the black background, but the diode is the triangular shaped thing with the label "D?" beside it. You will note that it is connected in parallel between the + and - terminals of the relay coil labeled "1" and "2" in the schematic, just as described in the other referenced document (coil diode). If you look at the relay module board, the diode is the small reddish brown cylindrical component with a black band on the end that has a "+" mark on the board.