I am getting/becoming more and more angry ...

[Anna232]

Does "getting" or "becoming angry with" somebody's words, actions, or behavior sound idiomatic?

I am getting/becoming more and more angry with his words/actions.

 

[teechar]

Yes, that's possible, but note that the comparative "angrier" exists in English.
Take a look at the ngram.

Google Books Ngram Viewer

Google Ngrams: becoming more and more angry, getting more and more angry, becoming angrier and angrier, getting angrier and angrier, 1800-2022

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