It seems that Ueshiba took it more or less as it was and incorporated it into his own training.
At least Kisshomaru trained, O Sensei observed classes.
Is there a strong Kashima Shinryu-influence in mainstream aikiken? I know that Yamaguchi-line aikido seems to practice Kashima Shinryu-influenced aikiken but outside of that lineage it really doesn´t seem that common.
I guess it depends on where you stand, but from my perspective its a strong flavoring. The primary hombu guy to bring Kashima Shinryu in seems to be Inaba Sensei. I am not sure if Yamaguchi learned from him, or also trained officially, but Tissier Sensei picked a lot of it up, and Gleason Sensei as well. These teachers were quite upfront about how they had found all of this great Aikido-like movement in Kashima Shinryu and for awhile they practiced it without re-branding.
(Eventually the Kashima Shinryu people got irritated with all of this and insisted that Aikido teachers stop using the name of their art without permission.)
I am not sure what influence Kashima Shinryu has had on Saotome Sensei's aikiken but their heavy, straight bokken with the solid wood tsubas were quite popular around Shobukan in the 90s.