Is it important for FR garment heraldry to be flame resistant?

The short answer from Oberon’s perspective is “yes”.
According to ASTM F1506-02a Section 6.1, “Thread, findings and closures used in garment construction shall not contribute to the severity of injuries to the wearer in the event of a momentary electric arc or related thermal exposure.”
Also pertinent is Section 6.1.1 “Sewing thread utilized in the construction of garments shall be made of an inherently flame-resistant fiber and shall not melt when tested at a temperature of 260°C (500°F) in accordance with Federal Test Method Standard 191A, 1534.”