Here, 'would go' in simple future tense is correct because it is used as the past form of will when reporting what somebody has said or thought. Here, 'he' said that he 'would go' for a walk in future (evening).
'Will' is used for showing that somebody is willing to do something or is used for asking somebody to do something. Example: Will you get up from that chair?
'Has been going' in present perfect continuous tense is used to indicate an action that started st some point in the past and may or may not be complete.
'Is' is used to indicate an action that is going on at the time of speaking.
Example: The child id going to the school.