There isn't a 'Sunkist' cultivar, at least not that I know of. They are simply Navel oranges grown by contract growers in Arizona and California.
It's the sticker that makes a 'Sunkist' a Sunkist. The most commonly grown and favored Navel cultivar is the 'Washington' Navel. I'd suspect that most Sunkist are Washingtons.

Purchase a nice, grafted Navel orange at one of your local nurseries.

Scubastan get a Washington Navel and grow it.
I suspect any fruit ripened on the tree will
blow you away with new found flavor and sweetness.
Maybe Sunkist picks them extra unripe for export.
They cant be as bad locally sold or you
wouldnt want one.

After the 83 freeze we only had Sunkist in Texas.
I hope we never see that again.

Better yet find a local Master Gardener and get their
recs on an orange. Maybe a non blood colored Moro?

Dittos that Sunkist is the name of the grower's co-operative, not the variety. I believe they grow a lot of Washington, also called Parent Washington, because many of the other varieties came from Parent Washington. There are now varieties that are a little earlier and some that are a little later. And of course the novel CaraCara which gets a little pink color. Most are "sports" where a branch from a certain tree, for what ever reason, just started growing differently, and someone noticed and started propagating it. Parent Washington seems to do this rather freely.
So, for best quality/flavor, some say the Fukumoto is the best, and it is an early one. For a late variety, Lane Late is good and well proven. All are very similar fruit, really only very subtle differences. I have:
Atwood
Desert
Fukumoto (early)
Lane Late
Thompson Improved (early)
Parent Washington
Cara Cara pink

Not True Sunkist is the only orange I can eat that I don't have an allergic reaction to. Any other Orange I need an epi pen. So there has to be some difference.

Sunkist is a trademark; not a variety; there are Sunkist lemons, oranges, grapefruits, etc. "Sunkist" is not a grower; they only pack and ship and put their mark on cooperative growers' fruits. As for an allergic difference, it could be that Sunkist packers use a different wax; but apart from that I don't know what could make a difference.