Bring a medium pot of well-salted water to a boil. Have an ice bath ready.
Boil the green beans until just crisp-tender, about 3 minutes. Add the okra and cook for 30 seconds. Drain in a colander and immediately transfer to the ice bath to cool. Drain the vegetables and pack them into the Mason jar along with the dill and garlic.
Heat a medium saucepan over medium heat and add the coriander seeds; toast until fragrant and a shade darker, about 2 minutes. Add the vinegar, sugar, red pepper flakes, cayenne, smoked paprika, 1 1/2 teaspoons salt and 1 cup water. Bring to a simmer, stirring until the sugar dissolves. Pour the brine over the vegetables. Add a little water to the jar to cover the vegetables if necessary. Cool to room temperature, then cover the jar and refrigerate for at least 6 hours and up to 3 weeks.