Is "funnest" a word?

Taken from Wiktionary:

Funnest is a regular superlative of the adjective fun. However, the use of fun as an adjective is itself still often seen as informal or casual and to be avoided in formal writing, and this would apply equally to the superlative form. Merriam-Webster, however, gives fun as an adjective without comment, and states that funner and funnest are ‘sometimes’ used. Because of the remaining stigma, most fun may be preferred in formal writing.

Given that every English speaker would understand you, it's fine. It's a word. Don't worry too much about what dictionaries say, they are trying to report on the language, not prescribe it.

"Funnest" has good English morphology. For instance, it doesn't begin with the glottal "ng" sound, which doesn't occur in English at the start of a word. That kind of thing would tend to spoil all chances of an utterance from becoming an English word.

It is derived from "fun", which is already an English adjective, and it is derived according to a rule that derives many existing superlatives. So you have here a good candidate for a word which could easily pass into usage among a group of English-speaking people, and evidently it has.

The only problem is that it's not widely used.

The human brain probably handles language not simply with with rigid rules, but through the memorization of a large number of special cases and exceptions based on examples and correction during language acquisition.

This is why numerous irregularities can happily exist.

Examples that are not heard are sometimes ruled out by native speakers as ungrammatical.

"Funnest" sounds strange simply because it's rarely heard, other than from children (who are usually going to be corrected to say "most fun" instead, thereby ensuring that they too will come to regard "funnest" as strange, when they will have long forgotten that they uttered it when they were small.)

On the other hand, "funner" and "funnest" are not so unheard of that it has not made its way into some dictionaries, such as Merriam-Webster.

If a word is in at least one major dictionary, it's safe to regard it as a word.

Some dictionaries may be more conservative than others, but, on the absolute scale, they are maintained by some pretty darn conservative people who will not too casually lend their support to a new word. If some of them think something is a word, that's probably good enough for the rest of us.