All good stuff and fully concur, with the exception that I would just put one layer (again, a loose covering not a 'wrap'). Cling film is also a good insulator and you want the heat out of the wound. You can continue to cool with running water in place.
Cling film gained favour as a burn dressing and furthermore in the outdoors as it can be used very effectively to immobilise joint injuries, is not effected by moisture, is inherently sterile, you can see wound infections developing over time, is quick and easy to apply yada yada yada but....
...is a real biatch to keep in your bergen or FAK. A 12" long roll is not hugely convenient to pack. We tried cutting a tube down but that often 'welds' the ends together. The food grade cling film is also pretty fragile. (we have all done the Rubiks game of
'trying to find the end' to get it started, and then when it does...it tears off in a frustrating taper!)
The solution? 'Stretch Wrap' or packaging wrap. Similar stuff but a few microns thicker, it is a bit more durable and the 6" roll is a lot easier to carry. These also come on a rigid cardboard tube which is wider than the wrap; this protects the ends which prevents it coming off in tapers.
I haven't found them available individually so we buy them in boxes of 10 from
Staples.