Can anybody tell me if there a single word which has the meaning 'to grow and flourish'?
I believe you're looking for thrive.
How about bloom / blossom ?
- to be in a vigorous state; thrive: a period in which art flourished.
- to be in its or in one's prime; be at the height of fame, excellence, influence, etc.
- to be successful; prosper.
- to grow luxuriantly, or thrive in growth, as a plant.
It kind of sounds scientific but I don't think it is inartistic as a word, if that is what you are going for.
I think it is pretty acceptable to think that as time passes by certain tastes of our mature and become more refine.
Although, I am not sure if any of these words really cover the 'flourish' part of your requirements.