Flushing with a good cleaner is necessary after each use (forward-flush, back-flush, flush). Just make sure you are confident that the tubing is clean with no remaining debris. After cleaning, flush with clean water. Ideally, if you can then dry the inside of the tubing then you can feel confident that nothing is going to grow in there during storage.
I would not store it with any liquid inside the tubing. Totally bone dry is best; the closer to that you can get the better (you could blow it out with an airhose to dry it if you have one; or even vacuuming it out should accomplish the same).
Running a little cleaning solution and sanitizer through it on brewday can help alleviate any concerns of contamination risks associated with it; and running some boiling wort through it just before chilling can provide extra insurance as well.
All that said, there's the RDWHAHB way of doing things: flush with water and put away wet - flush before next use and run boiling wort through it to sanitize.