Kim's dog and her cat are good friends, most of the time.

subject: Kim's dog and her cat

verb: are

The verb is correct.

You've identified the complete subject. Are you supposed to identify the simple subject?

Find the simple subject

Kim's dog and her cat are good friends, most of the time.

answer: dog and cat

Yes.

The subject of the sentence is "Kim's dog and her cat," and the verb is "are." In this sentence, the subject is composed of two nouns connected by the conjunction "and." The subject is talking about the relationship between Kim's dog and her cat, mentioning that they are good friends most of the time.