The easiest way to share a Swimlane Timeline custom Style is to use the ST Manage/Style/Copy Selected to a Folder option.  This will copy the custom style settings, and all other custom settings referenced by the style, to the specified folder. 

If you and your team have already set up, and are using, the ST Manage/Shared Folder then the ST Manage/Style/Copy Selected to a Folder option makes it even easier because it defaults to the Shared Folder location.