>>33446568engine.healmachineanim.asm:HealMachineAnim.palettes gets loaded into OBPals + 8 * 6, i.e. palette #6.
RGB 31, 31, 31
RGB 31, 19, 10
RGB 31, 07, 01
RGB 00, 00, 00
Remember that it applies to the flashing machine display as well as the Poké Balls.