EagleFiler supports mbox, the standard format for importing and exporting e-mail messages. Each mailbox is stored in a separate text-like file, and the mailbox files can be organized into folders.
Most e-mail apps have a command to export messages in mbox format. You can also export from Gmail to mbox format using Google Takeout.
To import mbox files into EagleFiler, just follow the regular Importing Existing Files instructions.