You can’t delete individual messages on Milyo. Once messages are sent, they are stored on our servers forever.
However, you can remove entire conversations by unmatching someone. When you unmatch someone, you’ll disappear from their match list and they'll disappear from yours.
To unmatch someone, go to your match’s profile > hit the ellipses icon (3 dots) located in the profile description > Unmatch. Note that unmatching is a permanent action.