It's really not that obscure in context.
Schjeldahl is talking about how the content of the photographs seem like the same snapshots everyone's uncle takes, and they even show off (flaunt) their seeming carelessness, but through the meticulously well executed craft of dye transfer printing, Eggleston transforms these everyday scenes into symbols (or perhaps icons) of their time and place.
There's a bit more there, which isn't needed to understand the sentence, but is interesting, if you happen to know it.
An icon in the context of Eastern Christianity is a very particular kind of symbol, because the perspective of any particular icon is always the same, no matter what the perspective of its visual context, so the icon provides a kind of window onto the plane of the divine for the viewer who is standing in the earthly plane. So to "iconize" these mundane scenes is to raise them from the level of representation to symbol in a way that provides a window onto the divine plane. They may not do it for you, but that's a separate issue from understanding what Schjeldahl is claiming.
"Synthetic gorgeousness," while simply speaking of the beauty of Eggleston's craft, also makes a nod toward the distinction between synthetic beauty and natural beauty. There's a hint of Decadentism (a movement in literature and the arts at the end of the 19th century, exemplified by J-K Huysmans' novel Against the Grain among other works) in this understanding of Eggleston. One characterization of the Decadentist movement was that it found beauty in artifice, and natural beauty in natural objects that appeared artificial, like the anthurium, a flower that looks like wax or plastic. Eggleston photographs things that stand out in their artificiality and even ugliness, but the artifice of his printing makes them beautiful, for Schjeldahl.
