Whisk together first 5 ingredients. Place chicken and half (about 1/3 cup) of the curry paste mixture in a large ziplock plastic bag. Reserve remaining mixture. Seal bag, removing any excess air, and massage mixture into chicken. Chill 2 to 24 hours, turning occasionally.
Preheat grill to medium-high (about 450°F).
Coat bell peppers, Fresno chiles, and shallots with cooking spray, and place in a single layer on grill grate. Grill bell peppers and Fresno chiles, uncovered, until charred, turning occasionally, 6 to 8 minutes. At the same time, grill shallots until charred, 2 to 3 minutes. Place bell peppers, Fresno chiles, shallots, and 2 tablespoons reserved curry paste mixture in a large bowl, and toss to coat.
Remove chicken from marinade; discard marinade in bag. Place chicken on grill grate, and grill, uncovered, until done, 5 to 6 minutes per side. Arrange vegetables and chicken on a platter; top with remaining curry paste mixture.