In order to do that, you'll have to open Allo on your Android device, access the Settingsmenu, tap Chat, and choose whether you want to "export messages from chats" or "export stored media from chats".
The most recent release of Allo, version 27, added an export feature so you can grab your chats and stash them safely for posterity.
Allo, Google's iMessage competitor is being shut down, and users will no longer be able to export older messages from the app.
Google is published a nifty little tutorial to help users save their Allo chat history before the chat service is officially shuttered. Google continues to invest in Duo, which recently got support for web video chat. You can download the v4.1.065 update from APK Mirror if it's not yet reached your device via the Play Store. It is on the same support page that the company notes "We're saying goodbye to Allo on March 12, 2019". Any media attachments you sent - such as pictures - will be downloaded in zip format. All of your messages will be completely deleted, though conversations you've had with Google Assistant will remain stored on Google's servers (you can delete them if you wish).
Google Allo isn't the only Google service that it is being discontinued this month. To get photos, videos, or any other files shared on Allo, you will have to use the media export option.
Allo was launched back in 2016 alongside Google's first-party video calling app, Duo.