How do you find archived messages on android?

If you want to check your Archived messages, just open your Messages app and access the Menu by tapping the 3 dots at the upper right. Then tap on Archived.

Where are archived text messages stored?

Archive text conversations, calls, or voicemails

You can archive a text conversation, call, or voicemail from your Google Voice inbox without deleting it. If someone replies to a conversation you archived, the messages show up in your inbox. Touch and hold the conversation, call, or voicemail you want to archive.