On occasion, it is possible to get a flare-up when cutting thicker acrylic, depending on the type of exhaust and wattage being used and the thickness of the acrylic being processed. If this happens, place a tray of water and sand under the acrylic to absorb the beam, which reduces the possibility of this issue reoccurring.
Increasing air flow around the cutting area can further reduce this issue by blocking the exhaust in the areas that are not being used.
To avoid excessive flaming, try laser cutting acrylic with nitrogen (nitrogen tank connected in place of the Air Assist). This is a great option for cutting thick acrylic because it displaces the oxygen at low psi (2-5), where air has to be at high psi (20-plus), effectively blowing bubbles in the molten acrylic and causing the edge to look white. This technique improves processing performance and keeps the edge from getting frosted, as long as too much psi is not pushed out.
-Josh Stephens, Trotec Laser