Preheat the oven to 350°F for the tortillas. Thinly slice the radishes into matchsticks. Roughly chop the kimchi. Cut the zucchini into sticks about ½ inch thick and 4 inches long. Drain and rinse the black beans.
Add the black beans to a small saucepan over medium-high heat and mash coarsely with a fork. Add ½ cup water and a pinch of salt and pepper and lower heat to medium. Cook beans until slightly thickened, about 8 to 10 minutes. Remove from heat and cover to keep warm.
Place a large nonstick skillet over medium-high heat with 1 tbsp olive oil. Once the oil is hot, add the cut zucchini. Cook until charred on both sides, about 8 to 10 minutes, and season with salt and pepper. Wrap the tortillas in foil and place in the oven to warm.
Halve the avocado and remove the pit. In a blender, combine the avocado flesh, lime juice, ¼ cup cold water, just half the cilantro, 1 tsp salt, and a pinch of pepper. Blend avocado lime crema until smooth.
Pick the remaining cilantro leaves from the stems.
To build your tacos, spread mashed black beans onto the warm tortillas. Top with chopped kimchi, charred zucchini, and sliced radishes. Dollop charred zucchini tacos with the avocado lime crema and sprinkle with remaining cilantro leaves.