Bring a large pot of salted water to a boil and cook the gluten-free fettuccine according to package directions, cooking 1–2 minutes less than directed for al dente. Drain in a colander and set aside.
While the pasta cooks, cut the chicken breasts into bite-sized pieces and season with a pinch of sea salt.
Heat the avocado oil in a large skillet over medium-high heat until shimmering. Add the chicken in a single layer and cook undisturbed 3–4 minutes until golden; stir and continue cooking 4–5 minutes more until cooked through. Transfer the chicken to a bowl and return the skillet to the stove.
Add the minced garlic to the hot skillet and sauté over medium heat 1–2 minutes until fragrant, taking care not to burn it.
Pour in the canned coconut milk and bring to a full boil, then stir in the rice vinegar, sea salt, and ground nutmeg. Maintain a gentle boil and cook 3–5 minutes to slightly reduce and thicken the sauce.
Add the cooked chicken and drained noodles to the skillet and toss to coat. Cook together about 10 minutes, stirring occasionally, until the noodles absorb some sauce and the sauce thickens.
Serve immediately. If desired, offer lemon wedges or grated Parmesan as optional additions at the table.