In a small bowl, mix oil, garlic, fennel seeds, 3 tsp sea salt (flakes preferred) and 1 tsp freshly ground black pepper. Rub over chickens. Cover and refrigerate for at least 1 hour and up to 1 day.
To make blackened chilli vinegar, prepare a covered barbecue for indirect cooking. For a gas barbecue, heat burners under the grate side on medium-high heat; leave burners under the flat plate off. For a charcoal barbecue, build a fire on one side of charcoal grate, leaving other side of barbecue empty, and let burn just until coals are covered with white ash (do not spread out coals).
Toss chillies with olive oil. Place over lit side of barbecue. Cook, uncovered, turning as needed, for 8-10 mins or until chillies are charred all over. Cool slightly on a chopping board. Close barbecue lid and leave on to preheat. Using a small knife, remove stems and seeds and scrape away some of loosened skin from chillies (leave some blackened skin intact). Coarsely chop. In a medium bowl, combine chillies, vinegar, extra virgin olive oil, shallots, sugar and 2 tbs salt. Set aside. (Refrigerate, covered, for up to 3 days; serve at room temperature.)
Place chickens on a wire rack set in a large rimmed baking tray. Place tray of chickens over unlit side of barbecue. Close barbecue hood and cook, turning tray 180 degrees halfway through cooking, for 1½ hours or until chickens are dark golden and an instant-read thermometer inserted into thickest part of thighs registers 74°C. Rest chickens on a carving board.
Carve chickens and transfer to platters. Sprinkle with oregano and serve with blackened chilli vinegar.