Is there any way of creating a "home-made" effect of shock diamond phenomenon that I could take a picture of? If so, How could I make one?
Sorry Dan. The answer is "NO". After learning up to some pretty depth regarding those tricky diamonds in air-crafts, I could answer this one...
Shock diamonds are also called Mach diamonds or Mach disks. We guys mention "Mach" ($v$ to $c$ ratio) only when something attains a good % of velocity comparable to the velocity of sound in that medium (which here is air). As Wiki says, these are supersonic wave pattern formations at the rear-end of a jet-kinda aircraft (at the nozzles). Ok, It also says that supersonic waves range from 1 to 5 Mach.
That "supersonic" property should be noted because these are seen only during blasts of gas (at a nozzle, a vent or artillery) at supersonic speeds which are impossible to attain while sitting at home and watching TV. In order to do such, you require a large area, loads of fuel and mainly "an Afterburner"...
Note: I mentioned that you can't only create those diamonds. But, you could do a lot of things in photography. Like, picturing some cool flame torches in oxy-acetylene (or an alkane) welding torch and do some tricks using whatever you've got good in Image FX. Or else, you could blend some to create diamonds like these people :-)
(Could I get a good reason for the down-vote..?)