1988 Kawasaki VN 1500 Vulcan not charging

I'm going through the same thing, go to www.vulcanforums.com and look up your model bike, there are already discussions about the how to ohm out the stator and and VR.

Sounds like you have a bad battery. Have you taken it off and tried to trickle charge it? Make sure you test it and watch to see how fast the voltage is dropping. I suspect though, that the batter is bad or your charging system isn't giving it any juice. If you charge the battery, it should still run for 20-30 minutes even if the charging system is bad. That way you know if it's the battery or the charging system. Good luck!

the stator will be inside the left crank-case cover.

not sure of this exact model but there will be a cover on the opposite side of your clutch, i do believe that this stator is bolted right into the stator but if its not it should be self explanitory once you get the cover off

If you are getting 13volt output and it revs and gets 14.5volts it would appear to be charging. As you would get a drop in voltage if it were not. Stator is there for working. Check your voltage relay as it may be sticking which would cause it to run on system and not be sending charge to battery. Poor ground would also keep battery from being properly charged

(I am the author of the reference thread on TriumphRat that wasposted by another respondent)

Not personally intimate with the Vulcan, but this is a 'conventional' motorcycle 3 phase stator energized by a crank driven magnetic rotor. 
The stator is connected in delta to the R/R. There should be NO measurable resistance from any of the three stator output terminals to engine ground - it should be completely isolated.   If you can measure a low resistance (not clear if your 0.2 ohms is from terminal to terminal or terminal to engine ground) then your stator is fried. 
Regarding the R/R connections - the third wire on the output is one of two functions (unfortunately without benefit of a schematic I cannot definitively conclude for you): either a 'voltage sense' wire, or in some Kawasakis they feed one phase of the stator output back out again for use in the starter cut/latch circuit. It should be reasonably easy to differentiate which it is. 
Good Luck! 

http://www.bikebandit.com/houseofmotorcycles/kawasaki-motorcycle-vulcan-88-vn1500a6-us-1992-clutch/o/m4620sch62090

this schematic list the brake breather. I hope this helps.

Behind the left engine cover. The engine must be almost completely removed to change it out.