The basic conclusion is that he have the understanding of the language you are able to speak, which it's different from "understanding what you speak".
And as far as can tell there isn't a restriction to just been able to read and understand.

My doubt is:
1- Since the creature have enough intellect, well it be able to understand a written message?
2- If the answer of (1) is no, by default, would you consider possible to teach the WildFire Spirit to read and write?

Thanks for you time and points of view!

It can mostly likely read,however have fun getting a sentient fire to write

Quote from TiradentesZ >>

The basic conclusion is that he have the understanding of the language you are able to speak, which it's different from "understanding what you speak".
And as far as can tell there isn't a restriction to just been able to read and understand.

My doubt is:
1- Since the creature have enough intellect, well it be able to understand a written message?
2- If the answer of (1) is no, by default, would you consider possible to teach the WildFire Spirit to read and write?

Thanks for you time and points of view!

I have a DM right now who's ruled "understand" does not imply "literate", but in general, literacy isn't explicit in the game rules - PCs are explicitly literate in any language they understand, but there's no such guidance for NPCs.  My personal interpretation is that everyone is supposed to follow that rule and 5E isn't intended to allow for illiterate creatures, but your DM can make any decision they want without violating the RAW.

I think the intention is for the spirit to understand verbal commands or have "conversations" and less actually learning the language. So I would say NO to (1.) and a NO to (2.) because I would think it strange for a "wild entity" to have or want to learn "meaningful scratching." Wouldn't it be like try to teach an elemental to read and write? Would they be able to understand the concept?

Illiterate elementals would mean djinn are illiterate, and that runs counter to every story ever about the djinn. 

The answer to this is not found in just one book. The Monster Manual goes into detail fairly early on.

Languages

The languages that a monster can speak are listed in alphabetical order. Sometimes a monster can understand a language but can't speak it, and this is noted in its entry. A"-" indicates that a creature neither speaks nor understands any language.

 But even without this paragraph, we know how it works. The wildfire spirit, "understands the languages you speak." That's it. If the druid says something to it then it will understand the druid. The stat block says nothing about being able to read or write. It's not written in the same way we assume that for player characters or other NPCs that just know a language. So, absent text expressly granting this ability, it cannot do these things.

That's it.

I don't think the conclusion of "understands the languages you speak." is "If the druid says something to it then it will understand the druid". He understand the language, doesn't matter if is the druid speaking or another creature. I mean, you conclusion would only make sense if the written was something like "Understand what the druid speak" then it would be linked to the druid speaking and not the language he speaks.

For my understanding the correct conclusion is "He knows/understand the language the druid can speak" and that brought me to the topic question: How far Knowing or Understanding a language put you on?
Following most of the responses I guess there isn't a RAW since they don't specify how literate should be approached. I'll see what the DM says...

Thanks guys!