Your sentence sounds totally natural to me. The two は in your sentence can be replaced by が depending on the context. I suppose the some others may have thought that the particle choices did not match the context. For example, the following conversation can be possible. （あなたは）犬は/が好きですか？ いいえ、(私は)犬は/が好きじゃないです。でも(私は)猫は/がすきです。 (In this conversation, 犬は sounds more natural than 犬が) The tricky thing here is; there is a subject-predicate relation between 私は and 好きじゃない, but 犬は/が is independent. I have looked up the reason before but the explanation was too complicated. But it seem to be grammatically correct. For example, http://w01.i-next.ne.jp/~g140179870/hagakobun.html

I think you can use both が and は in this sentence. When, I hear 私は犬はすきじゃない , I assume you might like the other aimals. When you use が, the sentence dosen't have such nuance. It's only my opinion.

At times it seems that everyone has a theory about は and が that differs from the theory everyone else seems to have. I've come to thinking that not even Japanese know really the "correct way". One of the reasons is that they are both used in more than one sense. Are all those uses "textbook" and higher level scholarly study correct? I don't know, but people seem to use them is varying sense. The way I understand, you could say 犬は好きじゃない meaning "I don't like dogs" though a bit awkward and would mean "I don't like dogs (among other things that I don't like either)". There are some explanations on wikipedia, but it is wikipedia, it might and it might not be fully correct: https://en.wikipedia.org/wiki/Japanese_grammar#Topic.2C_theme.2C_and_subject:_.E3.81.AF_wa_and_.E3.81.8C_ga

You can only have one は in a sentence. The は denotes the the topic of the sentence while が denotes the grammatical subject. These two are often the same in which case, the は replaces the が. In this sentence, the main topic, what your talking about, is "I" 私, but the subject is the dog. The dog therefore takes が. The sentence should be 私は犬が好きじゃない。 "As for me, I dont like dogs." Or more technically speaking, "As for me, dogs are not likeable" thus implying "I dont like dogs"