There is a way to upload/create multiple database connections to FME Server/Flow at once?

Its not documented in the REST API but there is the /fmerest/v3/namedconnections/connections/ endpoint.

Its pretty straight forward to figure out from using dev tools to capture your request in the UI then using that to programatically formulate requests to FME, for example:
 

{"type":"Actian Ingres","parameters":[{"name":"HOST","value":"1"},{"name":"PORT","value":"II7"},{"name":"DATASET","value":"1"},{"name":"USER_NAME","value":"1"},{"name":"PASSWORD","value":"1"},{"name":"SPECIFY_JDBC_CONN_GROUP","value":"NO"},{"name":"CONNECTION_STRING","value":"<Unused>"},{"name":"MASK_CONNECTION_STRING","value":"<Unused>"},{"name":"CONNECTION_PROPERTIES","value":"<Unused>"}],"name":"test","category":"DATABASE"}

Or create a simple workspace, with a single reader for every connection (I think I would only attach an Inspector to every reader, just to mae sure it works first), and upload that workspace. Then when uploading, make sure you check all the connections. Luckily that’s easy, just toggle the box before ‘Connections’.

This is actually a nice way to be able to test your connections too. A workspace which contains important connections can be run on a schedule. If a connection gets out of date you know about it and can do something about it.  

@virtualcitymatt Oh! Never even thought of that, but yes, that would be a very good use indeed! Could include Web Connections as well, and other services that are called by HTTPCallers for example. That’s a brilliant idea (why didn’t I think of that? 😉😄)