Aerospace and power equipment require precise temperature monitoring in extremely high-temperature environments, which often feature narrow and curved installation spaces. Since traditional thermocouples cannot provide both measurement performance and structural flexibility simultaneously, we propose a flexible fiber Bragg grating (FBG) temperature-sensing array. The sensor features a dual-layer composite packaging structure comprising an inner braided quartz-wool layer and an outer nickel-based alloy tube. Combined with a high-temperature annealing process, the packaged array was evaluated against a WRP-191 reference thermocouple. Over the investigated heating and cooling points up to 1000 °C, the maximum absolute indication error, max|T_FBG − T_ref|, was 2.02 °C and the mean absolute indication error was 1.25 °C. These quantities are comparison errors relative to the reference thermocouple and are not expanded uncertainties. The dual-layer design also allowed a minimum demonstrated bending radius of 22 mm, supporting deployment in confined and curved installation paths.