I would just like to point out that the Japanese is different from the English shown by Kakashi. What he actually says is 「別空間を口寄せしたとでもいうのか？」,or, "Are you telling me that she (Kaguya) summoned a different dimension/was able to summon a different dimension?!" Kakashi was not referencing Sasuke in that thought, but Kaguya's technique.
To answer the OP directly, I do not know where Sasuke received the personal summoning. No one does, it was just used as a plot device to show us the audience 1) that Sasuke at the very least always prepares his gear in a way that he can survive different situations, and 2) that he was willing to save Naruto before anyone else (thinking very rationally about the greater situation at hand, humanities survival.) Flying just so happened to be the necessary plot device to do it, especially as it was later shown that Naruto being able to float was essential to saving everyone (when Kayuga defeated said hawk's flying ability.) However, because the normal reader of manga here in Japan just accept these things without thinking to deeply about them (and I remind you that this manga is in our shounen magazine, target audience elementary and junior high school.) This is more a situation of Kishimoto's lax in storytelling towards older, who would actually discuss (unnecessarily deeply sometimes) things depicted.
I do very much agree that the hawk is a mystery, and we will probably never know where he got it unless it will be used as a plot device later. It should have been caught, and the only logical reason I can give is that Sasuke went out, found a really powerful hawk, and tamed it himself with his sharingan. He then made it make a contract, and thus he is the sole summoner of it. And, being something that he summoned since before he even got his rinnegan, it is now part of his animal path (from the moment Sasuke got his rinnegan, all of the things he summons will be considered animal path, and therefore his prior summons would all also become animal path summons) and the ripple on its eyes are really the rinnegan now (therefore being immune to mugen tsukuyomi.) Had he summoned Aoda, Aoda would have also had the rinnegan, but a snake would instantly fall into the lava and burn to death. Of course, this could all just be me making an example of how too deep answers are not that important, and all that was really considered when that happened was just because Kishimoto sensei has steadily, over the spand of 15 years, written both Naruto and Sasuke to be be so unpredictable (Naruto because of how he ALWAYS turns things around in highly unorthodox fashions, and Sasuke because of how EVERY time he returns from a long absence in the manga he returns with a new technique. Every time) that we can just suspend belief whenever they do pull something off.
What do you think?
