In an 8- to 10-inch frying pan over medium-high heat, stir coconut until lightly toasted, 3 to 4 minutes. Pour from pan.
Cut 4 equal slices, each 1/2 inch thick, from watermelon piece. Lay each slice on a plate. Cut off and discard rind from remaining watermelon; cut watermelon into 1/2-inch chunks.
Put watermelon chunks into bowl along with jicama, vinegar, and basil. Peel cucumber, cut into 1/2-inch chunks, and add to bowl. Mix and season to taste with salt.
Spoon salad mixture equally onto watermelon slices; sprinkle portions with toasted coconut.