Sending difficult-to-source messages in general?

Using TAILS from a public computer would probably work, as long as you are willing send the messages online. Keep in mind that people are unlikely to take prank messages from anonymous email accounts very seriously. (I have only ever gotten form letters from elected officials, and I send well-researched serious messages, so if they ignore that, they'll probably ignore anything from mad.homeopath@anonymity-friendly-email-service.com.)

There should be some way to order flowers or other objects that you can send with physical notes attached without creating an account linked to you, but it would probably be difficult to anonymously buy a prepaid credit card, I'm not involved in bitcoin-related stuff, and I don't think there would be enough of a market for bitcoin-based flower delivery for anyone to get involved in it anyway.

This sounds like a generally bad plan, though. It seems likely to end with your local newspaper's police report column making snarky comments about you.