I am not acquainted with Bruce self stick but if you want to use it as a floor "covering", go for it. Do you glue the seams or does it go down like self-stick tile squares? Just remember it isn't a permanent floor and is subject to moisture, sunlight, dents and scratches from furniture & dogs, wear & tear, etc. and will probably need to be replaced sometime just like carpet and vinyl. You may get a year and you may get 20 years depending upon the conditions. Make sure you wipe up all spills in the kitchen and hope your dishwasher, refrigeration pan, and plumbing doesn't leak and damage it.
I wonder about the self sticking part. There is nothing like a solid floor that is nailed or glued down, but on the other hand you may want to allow for expansion like other wood floor "coverings" like pergo. They float and allow for expansion although I personally don't think they expand much unless exposed to direct sunlight and/or humidity changes. One advantage of those floating floor coverings like pergo, is with a circular saw and a crow bar, it can probably be removed as fast or faster than carpet and pad when it is time to replace it. The glued stuff has to be scraped off. Good luck.