Is there a way to tell iOS mail app to put emails from specific senders in a special folder automatically?

Solution 1:

If you’re using an iCloud mail account then you can go to http://icloud.com/#mail

In the top right of the screen there’s a preferences icon — looks like a cog. If you click on that the preferences pop-over opens, click on Rules and from there you can configure some basic rules to put messages into specified folders.

Solution 2:

I have a method that works using archive folders within an IMAP or Exchange email accounts. Manually create your archive folders somewhere within your email folders list. The archive must be stored online, not locally. I use Outlook to create my folders manually, but i think it would work without Outlook as well like on your web access. Once the folders are created and you've previously moved messages to that folder, your iPhone remembers this. So in the future once you've previously moved messages to these folders, new emails you get from that sender sender can be moved there very easily by using the move message feature inside mail. A pop-up will appear with 2 options; the previously used folder to quickly move the message there, or an option to select a new folder. This usually works for different types of emails from the same sender as well, say you have a subfolder for "Orders" and "Shipping Notifications", it will remember which folder that email normally belongs. It's not automatic, and its not perfect, but very easy to do and pretty flawless.