Is "atone with" used properly here?

No. "Atone" is a verb meaning to make amends, e.g. for a sin or fault: "These crimes must be atoned for", "You must atone for your error".

Perhaps you mean "attuned with"? To be attuned with something is to be in harmony with it.

Thanks.
See Mr.Beans' Johnny English Reborn.

This makes no sense as written, and of course the sentences have no obvious connection with each other.

The second sentence would be better written using the phrase "at one with":
I'm very much at one with the animal kingdom.

Of course! That is the answer. The problem was a missing space.

atone with the animal kingdom.
at one with the animal kingdom

Kudos goes to McTag.
Thank you all.