Is "a very good read" grammatically correct?

Is it grammatically correct to describe a book or article as a very good read?

It is correct. Here read is used as a noun referring to the thing that is being read. Note that the noun can also mean the act of reading something. The two senses are similar enough that sometimes they are not distinguished.

The process by which a word that has previously functioned exclusively as verb but has been refactored as a noun in modern usage is called nominalization. Examples are:

• a hard sell
• a must have
• a new install
• an unexpected invite

I could invent new examples:

• My new suitcase is a heavy carry.
• His phone number is an easy remember.

Are constructions are grammtically correct? Well, that's a very difficult ask.

Here is a good article on the topic: Mighty Morphin' Parts of Speech.