Cut the seedless parts from the watermelon and put these in a blender, reserving any juice. Remove the seedy part from each wedge and place in a sieve set over a bowl. Press the flesh through the sieve (don't worry too much about getting it all), then transfer the contents of the bowl to the blender.
Blend, in batches if necessary, until smooth. Add the chilli and blend briefly. Serve in chilled soup plates and add ice cubes, if using, and extra chilli flakes.