The new manga chapter has proved that there was no massive chakra level improvement in Kakashi.
It says here that chakra transferred to Kakashi when he grabbed his hand:
Another example on how Bijuu's can transfer chakra by touch is when Naruto fist-bumped with Son Goku (4-tails)
So when Kakashi was inside the 9-tails chakra cloak some of Naruto's chakra transferred to Kakashi:
So Kakashi's chakra levels may have changed slightly but its not the massive leap everyone thought it was.
What do you think ?