The American Medical Assn. said it would not comply with a grand jury subpoena seeking the name of a doctor whose unsigned admission of mercy killing was published in the AMA's weekly journal. The Cook County grand jury subpoena seeks all AMA records concerning the essay that was published Jan. 8. Cook County officials became involved because the Journal of the American Medical Assn. is published in Chicago. Kirk Johnson, the AMA general counsel, said that journal editor Dr. George Lundberg had invoked the Illinois Reporters Privilege Act and the First Amendment and would not release the information. The Illinois act provides that someone seeking privileged information must apply to the circuit court to set aside the protection, and must prove that there is no other source.