Bring a large pot of water to a boil and cook the rice noodles according to package directions until just tender; drain and set aside.
Whisk together hoisin sauce, fish sauce, soy sauce, and lime juice in a small bowl; set aside.
Prepare the garnishes: mince the garlic, chop or julienne the cucumber, chop the mint, julienne or grate the carrot, slice the scallion greens, and chop the peanuts.
Heat the olive oil in a large skillet or wok over medium-high heat. Add the chicken pieces and cook, stirring often, until browned and cooked through, about 5 minutes.
Add the minced garlic to the pan with the chicken and cook briefly until fragrant, about 30 seconds.
Pour the sauce into the skillet and stir to coat the chicken; cook a couple more minutes until the sauce thickens slightly and the chicken is fully cooked.
Add the drained noodles to the pan and toss with tongs to combine and heat through; adjust seasoning with red pepper flakes as desired.
Serve immediately, topping with chopped cucumber, mint, carrot, scallions, and chopped peanuts, and offer lime wedges on the side.