How could Kakashi use Susanoo?
Aside from the obvious chakra problem - which has been shown to be a problem on previous fights (namely vs Deidara, IIRC) - there don't seem to be any plotholes, IMO.

As I've pointed out in this answer:  


Amaterasu, "representing the light of the material world"1, is performed with the right eye.
Tsukuyomi, "the nightmare realm, representing the world of the mind and darkness"1, is performed with the left eye.
Susano'o is "the strength of the tempestuous force that resides only within those of have mastered"1 both of the above techniques. 


Granted we haven't seen Kakashi perform any of those, but we haven't seen Madara perform them either, and he mastered Susano'o all the same-
That being said, I don't think Kakashi was able to perform Susano'o due to the Sharingan's copying ability, but rather because he now possesses both Sharingan.

As for the chakra problem, maybe the next chapter will shed some light on that, but let's also remember that Obito gave Kakashi both Sharingan not in his physical form, but only as a 'blob of chakra', and he may have transferred some chakra over to Kakashi on the process.



1Naruto: The Official Character Databook