Flourishing is an adjective because it is used to modify a noun:
- The flourishing economy (adjective)
I pronounced flourish (using the International Phonetic Alphabets) as: /ˈflʌrɪʃ/. There are two syllables with the stress on the first one, which becomes something like: FLUR-ish (the U is pronounced like the U in up). Another pronunciation is: /ˈflərɪʃ/ (something like FLER-ish, ER pronounced like -er in teacher).
If you want to learn more about the International Phonetic Alphabet, you can find a guide here: International Phonetic Alphabet and Phonemic Alphabets
Flourishing was first used in the late 14th century to mean “propsering, thriving” . It was used from the early 14th century to mean “full of flowers”. It is derived from the verb flourish, which came from the Old French floriss-, which was the stem of the verb florir, which came from the Latin florere, all meaning “to bloom, blossom, flower”.