The Collaborative International Dictionary of English v.0.48:

Flourish \Flour"ish\, v. i. [imp. & p. p. Flourished; p. pr. &
   vb. n. Flourishing.] [OE. florisshen, flurisshen, OF.
   flurir, F. fleurir, fr. L. florere to bloom, fr. flos,
   floris, flower. See Flower, and -ish.]
   1. To grow luxuriantly; to increase and enlarge, as a healthy
      growing plant; a thrive.
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            A tree thrives and flourishes in a kindly . . .
            soil.                                 --Bp. Horne.
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   2. To be prosperous; to increase in wealth, honor, comfort,
      happiness, or whatever is desirable; to thrive; to be
      prominent and influental; specifically, of authors,
      painters, etc., to be in a state of activity or
      production.
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            When all the workers of iniquity do flourish. --Ps.
                                                  xcii 7
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            Bad men as frequently prosper and flourish, and that
            by the means of their wickedness.     --Nelson.
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            We say
            Of those that held their heads above the crowd,
            They flourished then or then.         --Tennyson.
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   3. To use florid language; to indulge in rhetorical figures
      and lofty expressions; to be flowery.
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            They dilate . . . and flourish long on little
            incidents.                            --J. Watts.
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   4. To make bold and sweeping, fanciful, or wanton movements,
      by way of ornament, parade, bravado, etc.; to play with
      fantastic and irregular motion.
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            Impetuous spread
            The stream, and smoking flourished o'er his head.
                                                  --Pope.
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   5. To make ornamental strokes with the pen; to write
      graceful, decorative figures.
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   6. To execute an irregular or fanciful strain of music, by
      way of ornament or prelude.
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            Why do the emperor's trumpets flourish thus? --Shak.
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   7. To boast; to vaunt; to brag. --Pope.
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WordNet (r) 3.0 (2006):

flourishing
    adj 1: very lively and profitable; "flourishing businesses"; "a
           palmy time for stockbrokers"; "a prosperous new
           business"; "doing a roaring trade"; "a thriving tourist
           center"; "did a thriving business in orchids" [syn:
           booming, flourishing, palmy, prospering,
           prosperous, roaring, thriving]

Moby Thesaurus II by Grady Ward, 1.0:

89 Moby Thesaurus words for "flourishing":
   abundant, balmy, blooming, blossoming, booming, bountiful,
   brandish, brandishing, budding, burgeoning, bursting, bursting out,
   clear, copious, creative, crescent, dense, developed, exuberant,
   fair, fat, fecund, fertile, flaunt, flaunting, florescent,
   flourish, flowering, fructiferous, fruitful, fruiting,
   full-fledged, full-grown, fully developed, generous, going strong,
   gross, growing, grown, grown-up, halcyon, heavy, hypertrophied,
   impenetrable, in full swing, in good case, increasing, jungled,
   jungly, lush, luxuriant, mature, overdeveloped, overgrown, overrun,
   palmy, piping, plenteous, plentiful, pregnant, productive,
   proliferous, prolific, prospering, prosperous, rank, rich, riotous,
   rosy, seminal, shaking, sleek, sprouting, successful,
   superabundant, swarming, teeming, thick, thriving, uberous,
   undulation, unweeded, vigorous, wave, wave motion, waving,
   weed-choked, weed-ridden, weedy