As of now, the integration between Mattermost and Dropbox relies on third party setup such as Zapier and Integromat:
* https://zapier.com/apps/dropbox/integrations/mattermost
* https://www.integromat.com/en/integrations/dropbox/mattermost

It will be great to have a built in plugin to perform this functionality. For example, send a notification to a channel / direct message when a file is uploaded.