If my brother died and had life insurance but no named beneficiaries, how do I go about filing an affidavit to claim his insurance to pay for funeral expenses?

I am so sorry for your loss.  If the life insurance had no named beneficiary then it will be payable to the estate of your brother.  So in order to claim it as you say you would have to be appointed as the personal representative of the estate and open an estate account.  The insurance company will then write the check the "the estate of" and you will be able to pay funeral expenses with the funds.  Good luck.