Alliteration makes "The Flowers" more musical and memorable.
Take line 2. Love is positive and selfless, looking for ways to "wake the world to greater joy." This /w/ alliteration is gently musical, perhaps suggesting Love's tender touch. The alliteration in line 6 is similarly soft, helping to convey the sweetness with which Love spreads joy in the world:
And soon the Flowers, that Love let fall,
Consonance of those same /f/ and /l/ sounds adds to the effect:
And soon the Flowers, that Love let fall,
All those delicate, lilting sounds help to convey Love as a tender, graceful figure.
Contrast these sounds with those used in relation to Greed. The growing /gr/ of "Greed's hot grasp"
evokes Greed crudely crushing Love's flowers in his grip. In this way, alliteration helps to emphasize the juxtaposition between Love and Greed.
In the final stanza, alliteration suggests the vibrancy of Love's flowers. There's the sharp /g/ of "green" and "gold" in line 13 and the triple /r/ alliteration of "So red, so ripe, the roses" in the last line. These repetitive sounds turn up the volume on the poem, conveying a sense of the flowers' beauty and joyful abundance.