At this time, System Messages from Roblox can be deleted, but regular messages from other players cannot. If you would like to clear messages out to have a clean inbox, we do have the Archive action.
How Do I Archive Messages?
The Archive action will move messages from your inbox to your Archive tab. To archive a message, while viewing it, simply click the Archive button located below the navigation tabs.
Note: You can move messages back to your inbox later by finding them in the Archive tab, viewing it, and clicking the Move to Inbox button.