By slamming blocks of air with large amounts of oxygen into the attacking paper snowflakes, they are using adiabatic compression to create heated wind that surpassed the paper's burning point to ignite the paper blades. 
This is an alternate form of "Heat Storm". This is a type of magic that is another level higher than simply creating adiabatic compressed air blocks. Kasumi and Izumi can activate this high level magic while Nitrogen Storm is ongoing due to the boundaries of their Magic Power when they are Resonating together. Though the Saegusa Family originally being from the Third Institute, still it is a high level magic, but if performed by two or three magicians at the same time (like the Saegusa Twins; Saegusa Kasumi & Saegusa Izumi), it is a simple task.