I've no idea whether you can use the cleaning kit you have, but I imagine it's just a detergent anyway so can't see why it won't work. The CDA's aren't the most fun job to clean, firstly you have to get the filter out and the screws will no doubt have rusted and turn to mush as soon as you put a screwdriver near them. I had to use pliers or mole grips to get my screws out, get some stainless ones to go back in.
Cleaning is easy enough, but it's the re-oiling that I lost patience on, it's quite hard to evenly oil the filter, especially on the inside. I ended up over oiling it, but I left it overnight on newspaper for gravity to get rid of the excess oil. Put it back in, but not before you've taken the MAF out and plugged the hole. Go for a spin to get rid of any further excess oil. Not sure whether it's for real, but I'm sure the induction roar got louder when I cleaned mine.
CDA makes a fantastic noise ey?