Critical hits were only affected by speed in Gen I.
This really is luck. Just because Kangaskhan got a crit on one turn does not mean her chances of getting a critical on the next turn are any lower (is there have been no stat modifiers). All of her moves have the same chance of getting a critical hit, which is 6.25% without any modifiers.
I've experienced this before where my Oshawott got a crit in every one of its first 5 battles; it's all down to luck.