Oh, so it as just meant to bias threshold to below 2/3Vcc? The way you wrote your post made it sound like the R3 and R5 divider somehow were largely responsible for turning the entire 555 into a JK.
Actually biasing THRES below 2/3Vcc turns the 555 into a Set-Reset Latch. A J-K requires a clock, and is much more complicated.