「すごくおいしい！」が文法的には正しいです。
理由：「すごい」の連用形（福祉的用法）は「すごく」だから。
Because "sugoku" is the correct form of conjugation.

ちなみに、「すごい」の意味はもともと「とても恐ろしい・とても気味が悪い」なので、「美しい」や「かわいい」と一緒には語源的に不自然であるという見方もあります。
Btw, "sugoi" originally means "very scary, very creepy", so sometimes it's considered that it's etymologically unnatural if it's used with "beautiful" and "cute" etc.

But don't worry. Everyone can understand what you mean and even Japanese people don't know about this. You don't need to get nervous to use "sugoi" ;)