This article explains how to permanently delete text messages from your iPhone's Messages app. It also describes how to hide the Messages app from Siri Spotlight searches, and includes other solutions. The instructions in this article apply to iPhones running iOS 14 through iOS 11.
How to Permanently Delete Text Messages on iPhone
Text messages stick around after you delete them because of the way the iPhone deletes data. When you delete certain items from your iPhone, they aren’t actually deleted. Instead, the operating system marks them for deletion and hides them, so they appear to be gone, but they’re still on your phone.
When you sync with iTunes or iCloud, the items you marked for deletion are erased. If you delete a text and then sync your iPhone, the message is gone for good.
You can also take steps to make text messages hard to find. Deleted messages won’t show up in a Spotlight search if Spotlight isn’t looking for them. You control which apps Spotlight searches and which it ignores.