Dump and tip have different connotations. The tip is where one deposits refuse/rubbish. Whilst a dump and is a pile/collection of unwanted things, not necessarily rubbish.
It’s a small but often important distinction.
As a less confrontational reply: from my point of view “unwanted fly tipping” is talking about rubbish. The concept of depositing unwanted, yet usable, not rubbish, things somewhere is not something that would happen (outside of the rather recent disposable culture context).
As to your sentence (which is perfectly fine), the use of words avoids possibly confusing repetition. Atypical use would be preferred to “no fly tipping, take it to the tip”.
I suspect might be one of those regional things like scone/scone[1].
1. It’s pronounced “scone” and I will fight anyone that says otherwise!