Flourishing, the Duke of Milan and us (10)
I believe the answer is:
prosperous
'flourishing' is the definition.
(I know that flourishing can be written as prosperous)
'duke of milan and us' is the wordplay.
'duke of milan' becomes 'Prospero' (character in Shakespeare's The Tempest).
'and' is a charade indicator (letters next to each other).
'prospero'+'us'='PROSPEROUS'
'the' acts as a link.
(Other definitions for prosperous that I've seen before include "Doing well" , "Affluent" , "Wealthy" , "Rich" , "thriving" .)