Preheat the oven to 200°C (180°C fan) and line a baking tray with baking parchment. If you have a wire rack, place it on the tray.
Place the Flamin' Hot Cheetos in a large resealable bag, seal it and crush to fine crumbs using a rolling pin or a heavy pan. Tip the crumbs into a shallow dish.
In a second shallow dish, combine the plain flour with the salt and black pepper. In a third dish, beat the eggs until well combined.
Trim any excess fat from the chicken breast fillets and slice each into strips. Pat the strips dry with kitchen paper.
Dredge each strip first in the seasoned flour, shaking off any excess, then dip into the beaten eggs, letting any extra drip off, and finally press into the Cheetos crumbs until well coated. Arrange the goujons on the prepared tray or wire rack.
Lightly brush the coated goujons with vegetable oil and bake for 18–22 minutes, or until golden and cooked through (the internal temperature should reach 74°C).
Leave the goujons to rest for a couple of minutes before serving. Serve with ranch dressing, blue cheese dip or a cucumber yoghurt sauce, if you like.