There are at least three types of omission of く, which should be distinguished.
The "traditional western" euphoric change is called ウ音便 and is described in this question, this one and a chart in this page.
(y)u, etc. This sounds old-fashioned and elegant. While this is commonly heard in samurai dramas, only a few courteous elder people use this today.
- おいしくない → おいしゅうない
- くるしくない → くるしゅうない
In the (modern) Kansai dialect, instead of saying
ku, the vowel right before
k will be elongated:
- おいしくない → おいしいない
- くるしくない → くるしいない
- あつくない → あつうない
- からくない → からあない
- くろくない → くろうない (kurônai)
The "recent slangy" version is different from these. This pattern is typically found on Twitter and such and look like this:
- おいしくない？ → おいしない？
- やばくない？ → やばない？
- ひどくない？ → ひどない？
It's similar to the Kansai dialect, but no elongated vowel is employed. And I doubt this pattern is dialectal; I often see young people living in Kanto say things like these. I believe this is a very new phenomenon (it suddenly emerged in the last 5 years or so) among young people, and AFAIK this is mainly used as a question sentence: "Isn't it ～～?" I am in my thirties and I'm perhaps already too old to use this naturally :D
As for 美味しない in the tweet in question, the user is not a Kansai dialect speaker. So it's not archaic elegant 美味しゅうない, nor typical Kansai 美味しいない, but recent slangy 美味しない. I think most young people who say these are doing so more or less playfully, knowing it's not standard. For now I don't think this will be part of the formal Japanese grammar in the future.