This Bangkok Post article gives the lay of the land with respect to appellate review of military court decisions in Thailand. "Appeals have been allowed in the military court since April 1, the date martial law was officially lifted in most of the country, except in restive border areas. Cases filed with the court before that cannot be appealed . . . ."
Under the 1955 military court act, the court allows appeals and has three tiers like courts of justice. But when martial law is in effect, appeals are not allowed and the ruling is considered final to ensure full military discipline during critical times.