Stand the melon on one cut end and slice off the remaining rind.
Cut the melon in half lengthwise and scoop out the seeds.
Halve each melon half, so that you have four long wedges. Slice the wedges crosswise about 1/4" thick. Gently toss the melon in a bowl with the lime juice, red pepper flakes, salt and half of the mint.
Arrange on a platter, drape the prosciutto on top, and drizzle with the olive oil.
Sprinkle with the remaining mint and serve immediately.