The Kyokai website lists all the dojo affiliated with it.
Both Nishioka Tsuneo's line and the Fukuoka line are affiliated with the Kobudo Shinkokai.
Affiliation has absolutely nothing to do with authenticity or legitimacy. Neither the Kyokai nor the Shinkokai issue any kind of official validation. Both the Kyokai and Shinkokai are host to multiple lines of YSR, YSgR, HNIR and others, for example. There are groups that are clearly and openly not pre-Meiji (Daito-ryu, Aikido, Karate) and nothing like the typical "koryu" (Ryukyu Kobudo). The biggest factor in membership is if the particular dojo wants to pay dues and participate in events.
Josh Reyer
Swa sceal man don, þonne he æt guðe gengan þenceð longsumne lof, na ymb his lif cearað. - The Beowulf Poet