In the Cottonwoods

[fuzzyllama1]

In the Cottonwoods
 
In Cottonwoods the bluebirds sing
like all the world’s beneath their wings - I don't know if I like the sing/wing rhyme. I already know bluebirds have wings, tell me more about their voices. The rest of the stanza is about their voices, I think you should stick to that theme. 
with throats that won’t be choked with fear,
che-cheek my dear, che-cheek my dear,
I know you must be listening.
 
A moment’s silence for the king
who chirps, this is the only thing—
a vaccine for the atmosphere
and the Cottonwoods. - I don't like the king. I think that's what you're going for so I like this part a lot. This stanza breaks the poem in half, exactly how the king comes in with his chirp. It is demanded to be heard whether the audience wants it or not.
 
Its necessary evil stings - Necessary evil makes me think there should be a reason for the "vaccine", but you do not expound on that, unless I am missing something.
our every grandson’s neck, and brings
a swelling to the inner ear
that damps the last che-cheek my dear,
and tags the lofty bluebirds’ wings
in the Cottonwoods.

Your poem makes me long for childhood. I like it a lot and I'd like to see the Cottonwoods when the bluebirds are singing.