I am not able to delete single text messages in a conversation since updating to iOS 8
If you double-tap on a message rather than single-tap, up pops a "Copy/More..." selector, and hitting "More..." gives you the trash and forwarding arrow icons (along with the ability to select other messages to delete at the same time.)

If the icons do not apear, or if they stop apearing, there is something not working the way it does for me. Some people find that the icons re-appear after a restart (if only for a short time). Perhaps completely "quitting" the application would help? If you double-click on the home button, and then "upswipe" the Messages window does that have any effect when Messages is re-started?