My brother recently passed away and did not leave a will. He does have a 22 year old son. He has virtually no assets or debts but did have a tax return check. The Feds reissued the check to "Estate of". How do I (or his son) become the executor of his estate so that we can cash the tax refund check for his son.

Call the IRS or whomever issued the check. They will tell you what you need to do to have the check issued in the sons name. Since the son is of age he should call. He will probably just need to provide a death certificate and proof of relationship. He may only need the death certificate and his birth certificate. They'll let you know.

With no will ? Does he have a checking account that is in joint name with someone ?

But you will have to go to probate court and be appointed the executor ( actually the son will be the first choice so you will have to get his permision)