How to test a sample of cigarette tobacco for its nicotine content?
Unfortunately, nicotine analysis is prohibitively complicated and expensive for a home kit. The presence of other alkaloids similar to nicotine pretty much necessitates that somewhat expensive equipment (i.e. a gas chromatograph) is used to first separate out the nicotine prior to analysis (typically by mass spectroscopy).  

The only practical means for a layperson to test tobacco products for nicotine content is to out-source the work to a GC-MS equipped laboratory that routinely performs such analysis.