Yes, multiple Roman sources mention looting during the great fire at Rome in 64 CE.

Cassius Dio, Roman History 62:

Here men, while assisting their neighbours, would learn that their own homes were on fire; there others, before it reached them that their own houses had caught fire, would be told that they were destroyed. Those who were inside their houses would run out into the narrow streets thinking that they could save them from the outside, while people in the streets would rush into the dwellings in the hope of accomplishing something inside. There was shouting and wailing without end, of children, women, men, and the aged all together, so that no one could see thing or understand what was said by reason of the smoke and the shouting; and for this reason some might be seen standing speechless, as if they were dumb. Meanwhile many who were carrying out their goods and many, too, who were stealing the property of others, kept running into one another and falling over their burdens. It was not possible to go forward nor yet to stand still, but people pushed and were pushed in turn, upset others and were themselves upset. Many were suffocated, many were trampled underfoot; in a word, no evil that can possibly happen to people in such a crisis failed to befall to them. They could not even escape anywhere easily; and if anybody did save himself from the immediate danger, he would fall into another and perish.

Tacitus Annals 15.38:

At last, doubting what they should avoid or what to do with themselves, they crowded the streets or flung themselves down in the fields, while some who had lost everything, even their very daily bread, and others out of love for their kinsfolk, whom they had been unable to rescue, perished there, though escape was still possible. And no one dared to stop the mischief, because of incessant menaces from a number of persons who forbade the extinguishing of the flames, because again others openly hurled brands, and kept shouting that there was one who gave them authority, either seeking to loot more freely, or obeying orders.