This whole Plane Shift thing started because of Zendikar. It's hard to imagine a Magic plane better suited for D&D adventuring than the one that was conceived, from start to finish, as "adventure world." Making the transition from The Art of Magic: The Gathering—Zendikar to Plane Shift: Zendikar was thus perfectly natural.
Innistrad came next, bolstered by the happy coincidence of the Curse of Strahd adventure coming out close to the same time. Then with Plane Shift: Kaladesh, I got to stray a little further from the core D&D experience, presenting a fairly fast and loose take on reskinning D&D magic items into the aether-powered inventions of Kaladesh. And now we come to Amonkhet—a desert plane inspired by ancient Egypt, ruled by an evil dragon Planeswalker, and which features one small safe haven from an undead infestation. It is not a traditional D&D setting.
The trials of the five gods provide the most obvious structure for a campaign set on Amonkhet. A group of initiates from the same crop might go through the trials together, and those trials alone could form the entirety of a short campaign. To flesh out the experience, characters could also undertake missions on the behalf of gods or viziers: defending the Hekma, joining the gods on a hunting expedition in the desert, and so on. The campaign could get complicated with the addition of viziers, who normally do not go through the trials (unless they choose to), or if any or all of the characters become dissenters.
Perhaps the best way to think of an Amonkhet campaign is that it takes place against the backdrop of the five trials, rather than being all about the trials. The trials provide a structure and a sense of drama, but relationships among characters—and between characters and the rest of the world—are where the meat of the story unfolds. You could set your campaign in the period leading up to when initiate player characters undergo one of the trials, with the trial as a climax to the whole story. You could use the Trial of Solidarity and the Trial of Ambition as a framing device for the campaign, to explore issues of collective unity versus personal achievement. (Initiate characters would undergo the Trials of Knowledge and Strength on their own terms.) Or you could ignore the trials entirely and focus on dissenter characters trying to upset the social order of Naktamun.
As always, The Art of Magic: The Gathering—Amonkhet is the definitive resource for information about the plane. With this document, you can use that information to build a campaign with a minimum of changes to the fifth edition D&D rules, which you can find here. And even without the book, you can find lore about Amonkhet on the Magic web site.
Good luck in the trials!