Hi zakcat2001,
For help with deleting multiple conversations use the steps below found in the article here: Delete and recover messages on your iPhone or iPad
"Delete a conversation
- Touch and hold the conversation to open an options menu.
- Tap Delete
. - Tap Delete once more to confirm.
As long as the conversation isn't pinned, you can also swipe left over the conversation, tap Delete, then tap Delete again to confirm.
To delete more than one conversation, open Messages and tap Edit in the upper-left corner. Tap Select Messages, then tap the circle next to the conversations and tap Delete in the bottom-right corner."
You can also find helpful information for recovering a conversation if you accidentally delete one you may need in the guide here: Delete messages on iPhone
Cheers.