Learn Finnish: Mulla on hyvä fiilis.

Mulla is the colloquial (puhekieli) version of minulla ("I have" or literally "on me"). In spoken Finnish, the pronoun minä often becomes mä, and its "have" form (the adessive case) shrinks from minulla to mulla.

The English translation says "I'm in a good mood", so why does the Finnish use mulla on ("I have")?

In Finnish, you don't say that you are a mood or feeling. Just like with being hungry (minulla on nälkä) or cold, Finnish uses the possession structure. So literally, this sentence translates to "I have a good feeling". Because it's a "have" structure, the verb is always the third-person on, rather than olen.

Is fiilis a slang word? It looks a lot like an English word.

Yes! Fiilis is a very common spoken-language loanword from the English word "feeling". It translates to "mood", "feeling", or "vibe". The standard written Finnish (kirjakieli) equivalent would be a word like mieliala or tunne.

Could I say "Minulla on hyvä fiilis"?