Is it safe to take indomethacin, tylenol (acetaminophen) and allopurinol at the same time?

Check it out. You can use a drug interaction checker whenever you have questions about drug-drug interactions or drug - food interactions. Here is 1 option (Drugs.Com): Your pharmacist is also a good source of info.
Yes. Be careful though because Indomethacin and alopurinol are both processed by the kidney so combining them can cause kidney damage, albeit likely temporary. Check with your doctor about whether combining them is the best regimen for you and what your maximum daily dosages should be based on your other medical conditions and your baseline kidney function.