Well, oxygen itself isnt flammable, but it is what means that everything else can burn. So if the whole atmosphere was oxygen then things would be really easy to set fire to and then everything else flammable would set fire around them too.
When the Americans sent the first people into space when they were practising to go to the moon they actually filled the capsule that they were testing on earth with pure oxygen, there was a tiny electrical spark and the whole of the inside of the capsule burned really quickly, it was a very tragic accident.
The other problem is that too much oxygen is actually poisonous for humans so we wouldn’t be able to survive, unless it had always been pure oxygen, then maybe we would have evolved to breathe it.
I presume you to mean that there is only oxygen in the atmosphere. This would be a disaster to match no other. For billions of years the earths atmosphere has been stable with the same relative concentrations of gases. Plants evolved by having mechanisms that allowed them to use the carbon dioxide in the atmosphere. Remove the carbon dioxide and every plant in the world would die. Pure oxygen is a poison for the biology.