If using wooden skewers, soak them in water for 15 to 20 minutes so they don't burn on the grill.
Cut the halloumi into 2.5 cm (1-inch) cubes. Cut the peppers and onion into chunks about the same size so everything cooks evenly.
In a mixing bowl, whisk together the olive oil, garlic, oregano, lemon zest, black pepper, and chili flakes.
Add the halloumi cubes and vegetables to the bowl and toss gently to coat. Let sit for 10 minutes, no longer, or the salt in the halloumi starts pulling out moisture and the cheese turns rubbery once grilled.
Thread the skewers, alternating halloumi, pepper, onion, and pepper, leaving small gaps between pieces so heat reaches all sides.
Heat a 12-inch grill pan or outdoor grill to medium-high, about 200 C / 400 F. Lightly oil the grates or pan surface.
Lay the skewers on the grill. Cook for 8 to 10 minutes, turning every 2 to 3 minutes, until the halloumi has golden char marks on at least two sides and the peppers are softened with light blistering.
Remove from the heat and squeeze the fresh lemon juice over the skewers. Serve right away while the halloumi is still warm and soft in the middle.