Place the dried flat rice noodles in a large bowl and cover with very hot tap water. Soak for 20–30 minutes until pliable but still firm to the bite, then drain well and set aside.
In a small bowl, whisk together tamarind paste, fish sauce, light brown sugar, rice vinegar, and Sriracha (optional) until the sugar is fully dissolved. Taste and adjust for a balanced sweet, sour, and salty flavor.
Heat 1 tablespoon of vegetable oil in a large wok or 12-inch skillet over medium-high heat. Add the sliced chicken and stir-fry for 3–4 minutes until mostly cooked through. Add the shrimp and cook for 2–3 minutes until pink and opaque. Remove both from the pan and set aside.
Add the remaining 1 tablespoon of oil to the pan. Stir in the minced garlic and sliced shallot (or red onion) and cook for 30 seconds until fragrant. Push the aromatics to one side, pour in the beaten eggs, and scramble for 1 minute until just set. Break into bite-sized pieces.
Add the drained noodles to the pan, pour the prepared sauce over them, and use tongs to toss everything together. Stir-fry for 3–5 minutes until the noodles are tender and have absorbed most of the sauce.
Return the cooked chicken and shrimp to the pan. Add 1½ cups of bean sprouts and half of the chopped chives. Toss for 1–2 minutes until the sprouts soften slightly but remain crisp.
Divide the Pad Thai among four plates. Garnish with the remaining bean sprouts, chopped peanuts, and chives. Serve immediately with lime wedges alongside and extra Sriracha or chili flakes if desired.