I want to delete my stored messages from iCloud

With Messages in iCloud enabled, if you delete a message in one place, it deletes everywhere. 

On your iPhone, iPad, or iPod touch

To delete an individual message or attachment, follow these steps:

1. In a message conversation, touch and hold the message bubble or attachment that you want to delete.
2. Tap More.
3. Tap Trash , then tap Delete Message. If you want to delete all messages in the thread tap Delete All, in the upper-left corner. Then tap Delete Conversation.

To delete multiple attachments from a contact or conversation, follow these steps:

1. In a message conversation, tap the contact's name at the top of the screen.
2. Tap Info .
3. Select See All Photos
4. Tap Select, tap the images you'd like to delete.
5. Tap Delete, then tap Delete Attachment to confirm. 

To delete an entire conversation, follow these steps:

1. Swipe left over the conversation that you want to delete.
2. Tap Delete.
3. Tap Delete again to confirm. 

On your Mac

To delete an individual message or attachment, follow these steps:

1. Open a message conversation.
2. Control-click the blank area of a message bubble that you want to delete.
3. Choose Delete.
4. Click Delete.

To delete an entire conversation, follow these steps:

1. Control-click a conversation.
2. Choose Delete Conversation.
3. Click Delete.

Learn more about about deleting texts and attachments in Messages in iCloud. 

Despite your messages being stored or rather synced in iCloud, they can all be found in the Messages app and subsequently can be deleted there.