Gmail currently allows you to automatically forward emails from any address, but if you're looking to bulk forward old emails you have to to it manually. To solve this, Digital Inspiration outlines a way to do just that by using Google Docs.
This is handy if you're using web apps like Evernote or Tripit and you want certain types of emails from the past as well as the future to be forwarded to them. You can create your own two-column Google spreadsheet or use Digital Inspiration's template. In your left column you write your label. Your forward addresses go on the right. Once you have your columns filled out, run a script by clicking Tools > Script Editor > Triggers > Current Script's Trigger and then Add a New Trigger. Here, set the intervals you want the auto-forwarding to happen. Once it's setup, it will continue forwarding emails as they come in.
How to Auto-Forward Gmail Messages in Bulk [Digital Inspiration]