There's no H-D Service Manual for Ks... The 1st ever was for the 59 XLH Sportster.
There're also a few Shope Dope loose sheets from H-D for general specs and clearances, Antique Supply has republished them in 4 handy books that cover all the H-D years; not just K or KH.
The K or KH Riders Hand Book will cover all the basic maintenance:
If you want to go a bit deeper, buy one of the earliest Sportster Service Manuals, most of the info will apply...