The title "Lord of Cinder' is subjective, as Gwyn was Lord of Cinder during the first cycle, in which he linked the fire, and the player then becomes the Lord of Cinder, who renews the flame, or the Dark Lord, who brings the world into the age of darkness.
The definition of Cinder is the remnants of a fire, meaning the previous Lords of Cinder must have ruled over the first flame as it was fading. It could also be referring to those who renew the flame, and sacrifice their souls to maintain the flame for another age of fire.
Dark Souls 3's antagonist is apparently a resurrected Lord of Cinder. Whether this means there are multiple ones that have existed, it is unclear.
Through the belief that a Lord of Cinder is one who presides over the dying first flame, it must mean that each Lord of Cinder managed to overthrow the previous Lord of Cinder and install himself. This could very well include the previous player characters.
Gwyn is the only confirmed "Lord of Cinder".