The double negation of i-adjectives not only exists, but it is quite commonly used among us native speakers when expressing opinions indirectly.
Take 「おいしい」 ("tasty") for example, by far the most common double-negative form would be:
"(the food) is okay/passable if not great"
That sounds fairly indirect, doesn't it? The direct phrase would simply be 「まずい」 ("bad-tasting") or 「おいしくない」, which would often be considered too direct for the Japanese taste (pun intended).
We also say:
which means practically the same thing as 「おいしくなくはない」.
I do not think that careful speakers would use 「おいしくなくない」 with no particle between the 「なく」 and 「ない」 to mean the same as the two above. I would, however, not be surprised if I heard it in careless hurried speech.