I don't think that flooring piece will hold well. I've inadvertantly broken many a tongue off flooring planks while installing them.. not exactly the strongest thing ever. Its hard to tell in the picture, but if the fitment isn't super tight, then the cabinets will wiggle annoyingly on the wall. A traditional cabinet is fitted using a angled french cleat which guarantees a tight fitment flush to the wall like this:
I personally would either break down and buy the gladiator track, or put a 2x4 piece of plywood where you want to mount the cabinets. Screw the plywood into 2 or 3 studs, and screw the cabinets into the plywood. I personally put a screw in all 4 corners of cabinets or else I feel they shake too much. Mounting them to a track never feels stable enough for my satisfaction. Or you can make your own french cleat tracks. Ripping a 1x4 in half at a 45 degree angle would make a suitable track. I personally would put 2 french cleats, one on top and one on bottom or else I don't think it would feel stable.