There are some relevant older results in section 5 of part II (on semisimple elements), of the 1968-69 IAS seminar notes by Springer and Steinberg included in Lecture Notes in Mathematics 131 (Springer, 1970). In particular, their Corollary 5.17 shows that a supersolvable subgroup of a connected semisimple algebraic group consisting of semisimple elements must lie in the normalizer of some maximal torus (defined over the finite field in your set-up). I'm not sure whether there are any stronger results in the literature, but the discussion by Springer and Steinberg shows clearly that such questions are not straightforward to deal with in the algebraic group context.
As Marguax observes in a comment, being an $r'$-subgroup is the same as consisting entirely of semisimple elements.
Possibly more can be said in the context of finite groups of Lie type, using only finite group techniques, but it seems that the given subgroup $K$ consisting of semisimple (that is, $r'$-) elements must be of a rather special sort to embed in such a normalizer. ADDED: Keep in mind also that the normalizer of a maximal torus in the ambient algebraic group has a somewhat delicate structure in its own right, sometimes but not always a semidirect product of the torus and a copy of the Weyl group. (This has implications for the structure of the finite groups.) One standard reference is the paper by J. Tits, Normalisateurs de tores. I. Groupes de Coxeter etendus. J. Algebra 4 (1966), 96–116