It’s not possible to use Obsidian with a vault in Dropbox directly.
and (courtesy of @Synchronicity):
These are the five methods currently believed to work for syncing between devices if you’ll be including an iPhone and/or iPad:
• iCloud (NOTE: iCloud on Windows is known to cause file duplication issues as well as data corruption and loss, and the Obsidian devs and community strongly recommend that you avoid this combination.)
• Official Obsidian Sync
• Self-hosted LiveSync plugin
• Remotely Save plugin and various cloud services, including Amazon S3 or S3-compatible, Dropbox, OneDrive for personal, and Webdav
• Git with the Working Copy iOS app