If I create Story Map with Map Tour in it, how do I export data form map tour?
I believe the data will already by a hosted feature in your content.
When I select the story map form my content section I only see ribon with "Overview", "Usage" and "Settings" options. Non of them have data export or any other options.
What do you mean by data export? What do you want to achieve?
If it's a Story Map, go in and edit/configure the story and 'Publish' the story.
If it's a Map Tour, then it's a Web Mapping Application which is saved and then either viewed as-is or embedded in a story or other apps.
I want to have a local backup of the data I filled into a Story Map's Map tour interface.
It is both insurance from arcgis going down/ability to move my data and use it with different provider as well as being a GDPR compliance requirement.
@povilasid -- If you used ArcGIS StoryMaps to create your map tour story, you can use the Print option (in the ... menu in the header) to export the story as a PDF.
The classic Map Tour template doesn't have a print option, but you can export the data from the feature service as @DavidPike mentioned. Just go to the item page for the feature service (not the story map), and you'll see an Export Data option there.