Combine the honey, mustard, olive oil, lemon juice, cilantro, garlic, curry powder, salt, black pepper, and red pepper flakes in a large bowl. Add the chicken thighs and toss to coat. Cover and refrigerate for at least 30 minutes, up to 24 hours.
Preheat a grill or grill pan to medium-high heat. Grill the chicken until cooked through, 5 to 7 minutes per side.
In a large bowl, combine the cucumbers, peaches, cilantro, mint, lemon juice, and salt. Toss to combine.
Serve the grilled chicken with the peach salad. Garnish with additional cilantro and mint, if desired.
