There's no key Jasmine opens the door for you.
You really have to walk all through the Pokemon trainers o.O It should take about a half-an hour xD
Chat with our AI personalities
You need to have seen Jasmine in the Olivine Lighthouse in Olivine City first. You'll find her at the top floor of the lighthouse.
go up the stairs or use the elevator
The lighthouse is in Olivine city at the lower right corner of the city.
talk to jasmine in the lighthouse at olivine city and then go to cianwood and talk to the pharmasist
It is on Cianwood City Island. You have to surf there from Olivine City. (NOTE: the gym in Olivine is actually the 6th Gym battle so go to Cianwood Gym first) Before you go to Cianwood City make sure you visit the Olivine lighthouse top floor to talk to the Olivine Gym Leader about a sick Pokemon first.