While we don't offer a way to actually delete messages and conversations from your inbox, you can hide them.
Hiding the messages will only clear them from your view, and will not delete the DMs. Once you message that user again or they message you again, the DM will re-appear in your list of messages.
On the Mobile App
Go to your messages
Press and hold on the conversation you'd like to hide
An option will pop up to hide it:
