As far as I know the best way in which a Kshatriya man can die is in the battlefield and it ensures he goes to heaven. (Correct me if I am wrong)
What is the best way for a brahmin man to die ?
Although the best way for anyone of any varna to die is to remember Krishna at the time of death (Gita 8:5)
Those who relinquish the body while remembering Me at the moment of death will come to Me. There is certainly no doubt about this.
But anything specific for a brahmin man in traditional hinduism.