In Moodle web you can delete several messages at once. This cannot be done in the app, they have to be deleted 1 by 1.

In Moodle 3.4 there is an "Edit" option in the top right. Clicking it lets you select messages by clicking them. Clicking the "Delete selected messages" deletes all the selected messages.

In Moodle 3.6 you have to click a message to enable deleting. After that you can select other messages and delete them all at once.