1. Her husband, a kind, quiet gentleman, worked for HHS's public relations department.

2. Her husband, a kind quiet gentleman, worked for HHSs public relations department.

Question:
choose the sentence that is written and punctuated correctly.
50 - 50 I choose #1. flows better.

You're right.

A rough rule-of-thumb when you have two adjectives together: Put a comma between them if you could also use "and" between them.

Based on the sentence structure and punctuation rules, I can confirm that Sentence 1 is the correctly written and punctuated sentence. It follows the standard guidelines for comma usage, which is to separate adjectives that describe the same noun. In this case, "kind" and "quiet" both describe the noun "gentleman." The commas in Sentence 1 correctly separate the adjectives, making it grammatically correct. Sentence 2, on the other hand, does not use commas to separate the adjectives, which is incorrect. So, you are correct in choosing Sentence 1 as the correctly written and punctuated sentence.