I've been thinking up a way to make Radiants in 5e, and settled on attempting it with a Windrunner first. The goal was to utilize only official material rather than homebrew it (which would be pretty fun too, but not for this run)
I settled on a few things and just wanted to get some feedback.
First off all, 3 levels in Warlock.That nets you Pact Boon so you can bond a Sprite.You're also going to want to bond the Celestial as that best fits with the lore. Even if your DM isn't being super helpful I imagine you could RP this up. Skills can be chosen based on need and how RP heavy you're looking to go. I'm uncertain about what spells to get, there's a few from your patron and then there's an absolutely massive spell list.
Next I'd go into Tempest Domain Cleric.This nets you a whole new set of spells and a lot of them don't exactly meet the class fantasy. However, there is one important item that it does give: Stormborn. "At 17th level, you have a flying speed equal to your current walking speed whenever you are not underground or indoors."
With the 3-level investment in Warlock the only way I can see getting flight and wind manipulation is this way.
However, if the goal is for temporary flight (which is more canonical) then Storm Sorcerer may be the way to go as their spell list includes fly.
Additionally, it's worth noting that Warlocks and Sorcerers share are charisma-based, while Clerics are wisdom.
The last one I'm going to bring up is Paladin which have Oaths that fit very nicely into the whole Ideals of the Radiants. However they don't have a good Windrunner kit as far as I've seen. They'd be a better option for a Bondsmith or perhaps Truthwatcher.
Edit: After speaking with a D&D buddy of mine it looks like, with DM approval you could do the following.
Run Variant Human (or another race that gets a feat at level 1) and use that feat for Magic Initiate and get a companion. This requires DM approval, but you can take a Sprite and stat it/treat it as a hawk, the sprite part being aesthetic only. With that done, pick any appropriate class or class combination and RP the rest!