How could Kakashi use Susanoo? There are two reasons I have this query (spoiler alert!):


   Firstly, Obito didn't have Susanoo. Considering you need to awaken both Tsukuyomi and Amaterasu, while Obito never used even one of them, how was Kakashi able to use Obito's eyes to produce Susanoo? If he copied Susanoo, then how did he do that? Is it even possible to copy something like Susanoo?

 Secondly, not being of the Uchiha bloodline, he faces immense problems in using even a single eye for long periods of time. He almost lost half his chakra by making a lightning clone against Deva Path. On top of that, now he has both eyes after a long drawn battle fighting the likes of Zetsu, Obito, Madara and now Kaguya, how is he even supposed to stand?
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