Marinate chicken drumsticks in mixture of yogurt and half of the lime zest overnight.
Combine cucumbers, carrots, rice wine vinegar, sesame oil, sugar, and red pepper flakes in a large bowl. Allow to lightly pickle for one hour.
Remove chicken from yogurt, wiping excess off with hands and sprinkle with salt. Dip each first in egg wash, then mixture of corn flakes, breadcrumbs, flour, the other half of the lime zest, and coconut.
When oil is hot, add three breaded drumsticks. Cook until crust is browned and meat is cooked through. Repeat for remaining three pieces of chicken.
Serve two drumsticks each atop a bed of the cucumber-carrot pickles.