Spread the ciabatta on a baking pan in a single layer. Bake until dried out, about 15 minutes.
Meanwhile, toss the tomatoes with 1/2 teaspoon salt in a colander set over a bowl and let stand 15 minutes to drain slightly.
Heat the olive oil in a large skillet over medium heat. Add the garlic and red pepper flakes and cook, stirring, until fragrant, about 1 minute. Add the zoodles and a large pinch of salt and cook, tossing gently with tongs, until just barely crisp tender, about 1 minute. Transfer the zoodles to a large bowl, leaving the garlic oil in the pan. Add the balsamic vinegar and 1/2 teaspoon salt to the skillet with the oil and stir to mix.
Add the bread, tomatoes, shallot and basil to the bowl with the zoodles. Add the vinaigrette from the skillet and toss to combine. Transfer to a serving bowl and serve immediately.