Put the avocados in a food processor and blend until smooth (or simply mash with a fork). Stir in the onion, chilli and cream and season with the lime juice, salt and pepper. Set aside while you prepare and cook the calamari.
Put the flour and Cajun seasoning in a large freezer bag along with a little salt and pepper. Mix well. Add the squid to the bag and shake well to coat all the squid in the flour mixture.
Heat 1 cm (½ inch) oil in a frying pan over a high heat. Shake off the excess flour and fry the squid quickly in small batches for 1–2 minutes. Remove from the pan and drain on kitchen paper. Keep warm while you cook the remainder, then serve immediately with the avocado dip.