Combine the vinegar, sugar, 1/2 cup water, 1 teaspoon salt and the ginger in a small saucepan and bring to a boil. Cook, stirring, until the sugar dissolves, about 2 minutes. Let cool.
Transfer half of the vinegar mixture to a large bowl and add the carrots and daikon; cover and refrigerate until ready to serve.
Transfer the remaining vinegar mixture to a shallow baking dish; stir in the lemongrass, shallot, soy sauce and fish sauce. Add the chicken thighs and toss to coat. Cover and refrigerate 2 hours, flipping the chicken halfway through.
Preheat a grill to medium high and brush the grates with vegetable oil. Remove the chicken from the marinade, scraping off the lemongrass and shallot; season with salt. Grill the chicken until well marked and cooked through, about 5 minutes per side. Remove to a cutting board.
Drain the carrots and daikon; stir in the cilantro. Cut the chicken thighs in half. Toast the bread on the grill and spread the mayonnaise on both sides; sandwich with the sliced cucumber, chicken, carrot mixture and jalapeno. Serve with Sriracha.