Hello Bret,
You can do this with hooks, more specifically . afterInsert hook. Read more about hooks here , and how you can use it here .
Basically the idea is that you set up a hook that runs when data is inserted into a database, and that hook inserts the data just inserted (via wix code) to another database, and you can just chain afterInsert hooks to how many databases you want.
Hope this helps,
Majd