Start with this:
http://en.wikipedia.org/wiki/Flame_test That article also has external links that will provide you with more specific instructions. You will need all of the instructions, and some practice, to have a chance of success. Your last two paragraphs of questions lead me to believe that you think you are a few questions away from a prefect solution. You're not, you're days away from a slapdash procedure that's been lost to the annals of analytical chemistry prehistory. You're just lucky I'm old enough to have even heard of this sort of thing -- when I did flame AA in college, in the 1990's, the young kids didn't even know certain metals colored some flames.
I would suspect the best way to do it would be to shave a few metal filings, and dissolve the filings in analytical grade nitric acid. Vinegar is just ridiculous, the metal won't dissolve in such a weak, dilute acid. Farly inert metals, like silver and copper will shield any cadmium from even strong acids. No, the sample must go completely into solution, or you're not analyzing anything at all. The quoted articles tell you a bit about what sort of flame you need. Read that carefully, and don't trouble us to analyze further shortcuts you devise.
Please realize that sodium ions are ubiquitous and color any flame yellow, and if you only have traces of metals, any yellow color is suspect.
Now if you had a diffraction grating, and could get a spectrum off the flame, and you built standards -- saw the lines of a pure copper flame, and a pure cadmium flame, then you might have a useful diagnostic procedure. But that seems like a silly amount of work for a one-off test. You can see what you can get here:
http://jersey.uoregon.edu/vlab/elements/Elements.htmlWhy, exactly, is it impossible to check with the manufacturer?