Right, let's get the practical stuff out of the way first. If you're talking about 'Gate: Thus the JSDF Fought There', the novel series, it's a bit of a fragmented landscape for legal digital consumption. The original light novels by Takumi Yanai are published in English by J-Novel Club. That's your primary source for the ebooks. You can read them directly on their site with a subscription, or purchase the volumes from major ebook retailers like Amazon Kindle, Kobo, and Barnes & Noble Nook. They do a solid job of keeping the translation updated.
Now, the audiobook situation is trickier, and this is where I think a lot of people get tripped up. To my knowledge, there isn't an official, full-length English audiobook adaptation for 'Gate'. I've searched Audible and other major platforms a few times over the years, and it just hasn't materialized. Sometimes fan projects or unofficial readings pop up on YouTube, but those are a legal gray area at best and often get taken down.
Your best and really only legal bet for the core story remains the J-Novel Club ebooks. It's a shame about the audio, because some of the tactical dialogue and the sheer chaos of the gate battles would be fantastic in that format. I just re-read the Ginza incident the other night, and the way the JSDF's initial confusion is written is so visual, it practically begs for a good narrator. Maybe one day.