Both are correct, but slight difference in meaning. If you are talking about something that they usually do than the first sentence is better. "What do your kids do at the weekends?" "Oh, generally they go fishing together." If you are talking about something that is happening now second one is better. "Where are you kids going?" "Oh, they are going fishing together."

#1 "They go fishing together" is correct and natural, but #2 is awkward. The general pattern is "go fishing," "go camping," "go sailing," "go skiing," and so on. More information here: http://www.eslcafe.com/grammar/verbs_other_verbs08.html

Second one is correct