Fire radical on the left marks 熄 as a fire-state verb - to extinguish or go out. Mnemonic: when fire 火 ceases to breathe 息, it dies down. Same radical drives 烧 (burn), 烤 (roast), 烟 (smoke). Position-left fire is the standard for actions on flame.
息 supplies the sound directly - xī with matching tone - and contributes a strong semantic flavor: the breath of fire ceases, the flame rests. This double-motivated pairing makes 熄 unusually transparent. Same character keeps standalone xī reading in 休息, 信息, 消息.
