It's an unfortunate tendency in textbooks on Lie algebras to assume that the base field is $\mathbb{C}$ even though virtually everything done in the classical structure theory and finite dimensional representation theory remains valid over an arbitrary algebraically closed field of characteristic 0.  For the theory of affine Lie algebras the book by Kac is an essential foundational source, but a possibly more readable textbook account of his ideas was given by Roger Carter in his 2005 Cambridge University Press book *Lie Algebras of Finite and Affine Type*.   Though Carter also tends to work by default just over the complex field, it's reasonably clear throughout that the arguments used are purely algebraic.  

Concerning the introduction of twisted affine algebras (as in Carter's Chapter 18), there may be slightly different viewpoints.   But for example Carter initially classifies generalized Cartan matrices and related data, then shows how to realize suitable Lie algebras having that data.   In the process only the graph automorphisms play an essential role.  

Maybe there are good alternatives to such books(?), but it's worthwhile anyway to consult Carter's book in order to clarify other issues you may encounter when reading denser parts of the Kac book.    In principle they are both talking about the same objects.