Among the crimes and vices of Emperor Elagabalus, the Roman historian Cassius Dio also lists eating flamingo brains- what is the significance of that?

First:

It is important to remember that often historians would inflate, distort or fabricate stories about emperors they didn't like. Often, when you read a "primary source" (sometimes actually written decades or centuries later), the fantastical and horrifying things Roman emperors supposedly did really can't be proven. Sources are often suspect, and in the Roman context, it pays to scrutinize anything you read about an emperor.

One source on that: Ernst Breisach, Historiography: Ancient, Medieval, and Modern, 3rd ed. (Chicago: University of Chicago Press, 2007)

This is not to say that Cassius Dio was wrong about Elagablus eating flamingo brains. It just means the sources should be scrutinized.

Second:

It is extraordinarily difficult to summarize Roman culture in a Reddit post. Rome was a complex city/republic/empire. It changed a lot over the 800 or so years people often regard as "Ancient Rome". It melded with lots of cultures and the history books are filled with lots of people. Some elements of their culture were directly contradicted by others, like every culture.

To crudely summarize, Romans were conservative. They were not fans of unhinged debauchery, licentiousness, drunkenness, gluttony, and so on. They frowned on men who dressed up as women, like Elagabalus himself. The sources may not be totally reliable, but if you take them in the aggregate, it's reasonable to conclude that Elagabalus was sexually and socially deviant.

This account, which sounds like it would be similar to that of Cassius Dio, provides more info: http://cabinetmagazine.org/issues/8/lampridius.php

For the Romans, eating flamingo brains would be unnecessary and inexcusable luxury. Romans wore simple togas, ate simple food, and won a lot of wars. Throwing decadent, luxurious parties was a sure-fire way to get people to hate you.

Notably, the perception of Elagabalus as self-indulgent and depraved has been helped along by modern historians. Gibbon, as an 18th century British male, probably wasn't crazy about flamingo-eating orgies, either.