Cut cucumber into chunky half-moons, then scrape out the core. Place cucumber in a medium bowl with vinegar, honey, chile flakes, and salt; set aside to pickle for 10 to 15 minutes.
While the cucumbers are pickling, toast hazelnuts in a medium skillet over medium heat until browned and fragrant, 5 to 10 minutes. Remove from the skillet and chop coarsely when cool enough to handle.
Slice halloumi cheese into 3/8-inch slices and place in a nonstick skillet over medium heat. Cook until crisp, 2 to 3 minutes per side.
Mix chopped hazelnuts and mint into the pickled cucumbers. Add halloumi and figs and toss to coat.