Combine ground flaxseed with 2 Tbsp water. Let sit for 10 minutes.
Drain and rinse the chickpeas. In a food processor, combine the cooked quinoa, chickpeas, panko breadcrumbs, BBQ seasoning, ketchup, flaxseed "egg" and 1 tsp salt. Blend until well mixed, scraping down the sides of the food processor as necessary.
Divide the burger mixture and press firmly to form 4 patties, each about 3/4 inch thick. Refrigerate for 15-30 minutes before cooking (optional)
In a nonstick skillet over medium-high heat add 1 Tbsp oil. Once the oil is hot, add the BBQ chickpea burgers and cook until crisp, about 5 minutes per side.