How can Kakashi use Kamui and Chidori so much during the Ninja War
He spams Kamui's and does get the side effects later.

In episode 418, right before Madara fights Gai. Kakashi mentions to Minato how bad his eyesight has become, and that he needs to get closer to use kamui (on one of the truthseeker orbs). During the fight with Pain we see this as well. When he uses his last kamui, blood flows from his eye due to overuse.

As for the 5 chidori's, that shouldn't be the problem with Kurama's chakra.