Slateport City doesn't have a gym.
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you sail with mr briney, to dewford, deliver the letter and beet the gym, then sail to slateport.
Vermillion City is in Knato and Slateport is in Hoenn; you can't.
Board the Ship which says Slateport city in Hoen
After beating the 2nd gym leader you need to see steven in the cave in dewford town if you have not already if you already talked to steven then talk to mr briney and go to slateport city from here go north to mauville city and beat the 3rd gym leader there.
In Slateport City, the contest hall is close to the northern exit, just to the left of it.