Yes — amoxicillin (an antibiotic) and Tylenol (acetaminophen, a pain/fever reliever) work in completely different ways and are commonly taken together, but stay within the acetaminophen dose limit and check with your pharmacist.
Amoxicillin is a penicillin-type antibiotic that fights bacterial infection, while Tylenol's active ingredient, acetaminophen (paracetamol), relieves pain and lowers fever through an unrelated mechanism, so they are not expected to interact. The NHS amoxicillin interactions page and the MedlinePlus amoxicillin page do not list acetaminophen/paracetamol among medicines that interact with amoxicillin (the drugs NHS flags to check with a pharmacist or doctor are methotrexate, warfarin, probenecid, allopurinol, and other antibiotics). In fact, acetaminophen is often used precisely to manage the fever or aches of the infection the antibiotic is treating. This is general information, not a personal safety clearance.
Follow the dosing on each label and do not exceed the acetaminophen limit (for most adults, no more than 3,000–4,000 mg in 24 hours; follow your product's label and any doctor's advice). The biggest real risk is accidental acetaminophen overdose from "stacking" — many cold, flu, and combination pain products already contain acetaminophen, so read every label and avoid taking two products containing it at once. People with liver disease, who drink alcohol heavily, or who take other acetaminophen-containing medicines should be especially careful and ask a clinician about a safe dose. Finish your full amoxicillin course as prescribed, and tell your doctor or pharmacist about all other prescription, over-the-counter, and herbal products you take. Seek medical care for signs of an allergic reaction to the antibiotic (rash, swelling, trouble breathing), and contact a professional if you are unsure about combining your specific medicines or doses.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.