Is a greek word commonly translated as happiness or welfare; however, "human flourishing" has been proposed as a more accurate translation?

The word your question is talking about is "eudaimonia."  I'm writing that in English letters -- not sure if the Greek version will appear here properly, but I'll try:  εὐδαιμονία
The word was used especially by the ancient philosopher Aristotle to describe a "well-spirited" life (that would be a sort of literal translation based on the etymology of the word).  Aristotle spoke of human happiness (or yes, "flourishing" is probably the better term) as the goal of human existence. We reach this goal by living a sort of life in accordance with the kind of beings we are.  The idea of eudaimonia was central to Aristotle's ethics, or his approach to the right kind of life for human persons to strive for.