Always nice to see new people dip their toe on Dothraki. Welcome, pinkunicorn.
anha lekhaan ki dothraki
That's not terribly close, though it is, in a way, an interesting attempt. I'm not sure, if you are just very very beginner, or if you are trying to find an interesting way to express the idea.
Anha ezzok anhaan Dothraki lekh
That is closer (which is no wonder, since Hrakkar has been around for quite a while). One clear error is with "Dothraki lekh". "Dothraki" as a language is in Dothraki lekh Dothraki, language of Dothraki. "Dothraki" is in genitive and genitive always comes after the noun it modifies.
Also, lekh should not be left in nominative. If you use ezzolat right, lekh goes almost certainly into accusative, which is lekhes (animate to distinquish it from "tongue").
Ditranstitives are tricky, though, and I'm not sure, how ezzolat would work. We have two objects, the person taught and the matter taught. Almost certainly one goes into accusative and another one is dealt in some other way, either with preposition or some specific case without preposition.
Then there's the matter of Dothraki reflexive. Dothraki has a special way to deal with "myself", nemo. If the person taught is in accusative, or if nemo just seeks the right object role by what makes sense or what is ommitted, you won't use a repeat of anha, you use reflexive. But because the ditransitive, it might be that nemo just does not work.
So for this idea "teach myself" idea we have something like
Anha nemo ezzok lekhes Dothraki. (lekh main object, but reflexive works)
Anha nemo ezzok lekhi Dothaki. (lekh not main object, here I'm trying on the "topic class" genitive, but that's just a stab in the dark)
Anha ezzok anhaan lekhes Dothraki. (lekh main object, and reflexive does not work)
The straightforward "I'm learning Dothraki" is not that straightforward either, because there's also the old problem of choosing the "learn" word. I think ezolat should work, though, so going simple, the sentence would be
Anha ezok lekhes Dothraki.