"Sounds almost like" vs. "almost sounds like"

Both structures are fully grammatical. There is a very slight difference, not really in meaning, but in emphasis:

That sounds almost like a command.

This puts the emphasis on "sounds".

That almost sounds like a command.

This puts the emphasis on "almost".

Both are grammatically correct.

I think that in your specific example, most English speakers would have difficulty saying what the difference in meaning might be.

But if you were to change the verb:

He almost barked like a dog. (Meaning he did not bark)

Vs

He barked almost like a dog. (Meaning he barked, but maybe he sounded like a seal.)

Those have very different meanings.

My best guess to explain this is that "sounds like [...]" is a phrasal verb, while "bark like [...]" is a verb followed by an adverbial phrase. Some would people would say that "bark like" is incorrect. They might object to "like" and "as" being used interchangeably. They would prefer "He almost barked as a dog." or "He barked almost as a dog."