You can either purchase the flamethrower or wait until you are given one during a main mission. If you wait until you receive it for free (which I suggest you do), your mission is to burn some fields of marijuana. Simply do not burn the fields and keep burning enemies. As far as I could tell, enemies were infinite until you burn all the fields.
*Note- the mission to burn the fields is given to you after you meet the man in white in the shanty town.*