I had done research and had not found any way to do this. I began testing it on the Verizon Cloud App on a Samsung Galaxy S6, an iPhone 6s, and HTC Desire 526, a Samsung Galaxy Note 4, and a Motorola Droid Turbo 2, (all test phones I have) and found a way.
Delete Messages/Calls from Verizon Cloud: To do this first place the phone in airplane mode and turn on WiFi to prevent new messages from being lost. Launch the Message+ application and delete the messages you dont want in the cloud. For all messages simply select the bubble to the right and hit ALL and then TRASH. Then go into the VZCloud app and go to Settings>What To Backup>Select ONLY Messages and/or Calls. Go Home on the app and do a backup. Now the messages and calls you deleted from the phone will be deleted from the cloud.