The Japanese slang スルーする has significantly positive nuance by itself, compared to Japanese 無視する. People who are good at net slang consider it to be something difficult to master. There is even a word スルー力【りょく】 or スルースキル, which is the important skill to survive the information era.
This is not surprising, because スルーする was probably derived from succor jargon スルーパス, which is another 和製英語, meaning a difficult pass penetrating the defense. You can see an example of typical 華麗なスルーパス at YouTube.
So ever since スルーする was born, 華麗に and スルーする have been used together very frequently. You can safely call "華麗にスルー" a set phrase.
So what is this "art of ignoring?" When can you ignore something nicely? Here are some examples.
In this conversation, B recommends that A should not respond to the troll. He knows that ignoring a troll is sometimes difficult, but B expects A to exercise his "skill of ignoring".
In this case, A could have directly responded to B's joke by saying 「カレーは飲みものじゃない！」, but didn't. Intentionally ignoring B's joke made B laugh instead. (Such "gag by ignoring gag" is sometimes referred to as ボケ殺し, and certainly is technical if done intentionally)
This is a sarcastic usage of 華麗にスルー. This 華麗に emphasizes his surprise that his advice was totally ignored.
This is naturally-sounding (though slangy) to me, and I believe no one would question "どこが華麗なんだ?". But now I think this 華麗に means almost nothing any more. Because 華麗にスルー is a set phrase, such things can happen. If I must, I would translate this 華麗に as "dare".
In the example of Steins;Gate, if 凶真 had said 物理的タイムトラベル jokingly, my second example would be the closest. But I think he said this rather seriously, so "because スルー is frequently used with 華麗に" would be the only explanation.