The easiest way to import a document into Speechify is to upload it through your Google Drive, DropBox, or iCloud. Please check this article for more details.
While you're on it, make sure you have a strong and stable internet connection and you're in the active foreground. That means you have to wait while it's processing and your phone screen is not locked until importing is done.
You may also try the usual basic troubleshooting steps - reboot your phone, update the app to its current version, reopen it, and try to import your file once again.
If the problem persists, drop us a message via "Message us" from your Speechify app.