Music
Due to the Front Mission 3D Remake (released in 2022), I can't host any music files here for Front Mission: Gun Hazard. If you were wondering, yes I did receive a takedown notice from Square Enix for my Front Mission music files. Although I don't know why Gun Hazard was included with Front Mission 1st's music. Maybe it was just collateral, or perhaps Square Enix has some secret plans to officially re-release or even localize Gun Hazard.
Music Streaming
Square Enix added the soundtracks for Final Fantasy, Mana, and SaGa to popular music streaming platforms. We'll likely see Front Mission 1st Remake's soundtrack added some time after its official release. However, I don't think we'll ever see Gun Hazard's soundtrack added. All I can do is offer this YouTube shortcut to find Gun Hazard soundtracks that fans have uploaded to YouTube. You could also try the Extracted Game Music option towards the bottom of this page.
Fan Music
The best place to listen to Gun Hazard fan music is at OverClock ReMix. They have also uploaded their music to YouTube. Although Gun Hazard is a pretty obscure game so there's not much fan music available.
Album Covers
Here's the official soundtrack cover. I also made one based on the title screen.
Extracted Game Music
The fan base has gone a long way with emulation. In the early 2000s, they came up with 'extracted game music' (a.k.a. chiptunes). They extracted the programming of the music from every classic video game and built digital soundtracks with them. With special music players, you can play these music files as if they were MP3s. And they're far better quality than MP3 because it's the actual programming of the song that you're listening to! In this realm, Super Nintendo music is under the 'RSN' file format. Music players that support RSN can be found on any device: Windows, Android, iOS, Mac, and Linux.
My favorite feature about this music is how small it is. Gun Hazard's RSN soundtrack is around 300 KB while an MP3 soundtrack is around 400 MB! So you could quite literally have hundreds of classic gaming soundtracks on your iPhone or Android phone, and barely make a dent in your phone's storage.
If you want to learn more, read my tutorial for Extracted Game Music. My tutorial also provides links where you can download RSN music. Extracted game music can be converted to MP3, too. My tutorial provides directions on that process.