People do not naturally avoid flames on Shabbat: Pesachim 11a
Lighting a fire as one of the "Father" forms of forbidden melachah, or standing on its own: Shabbat 70a; Pesachim 5a-b; Keritot 20a-b
Lighting a fire perhaps having a punishment of a sin offering only, and not Divine Ex-Communication or Death, even if done intentionally: Shabbat 70a, 153b
Burning something in a destructive manner: Shabbat 106a; Keritot 20a-b
Burning something for the ashes: Shabbat 106a
Melting lead to carry out the capital punishment of Burning: Shabbat 106a
Using a fire lit by a Nochri: Shabbat 122a-b
Cases
Placing a bowl of oil in position to drip into an oil flame; someone may accidentally take oil, which will be indirect Extinguishing: Pesachim 11a
Reading by the light of a candle, where it is far away: Shabbat 149a
Teaching children on Shabbat: Nedarim 37a-b
Turning coals, so that the now-lower ones are extinguished and the now-upper ones are ignited: Keritot 20a-b
Regarding intending to extinguish a flame, if it actually ignites: Keritot 20a-b
Prohibiting removal of more than miminal food from a fire, lest a person come to extinguish the fire: Shabbat 117b
Placing a cover on a vessel to prevent it from burning, while removing it from a fire: Shabbat 120a
Making a wall of old or new [easily burst] vessels, which or empty or filled with water, before a fire: Shabbat 120a, 120b
Soaking the non-burning end of a burning item in water: Shabbat 120a-b
Extinguishing is relevant to a wood coal, not to a metal "coal": Shabbat 134a [See Rashi "Ve'Ayn"]
Turning coals, so that the now-lower ones are extinguished and the now-upper ones are ignited: Keritot 20a-b
Raking coals, causing them to ignite, when only trying to produce warmth: Keritot 20b
