Duraflame firelogs are designed to burn for up to four hours at a time without the benefit of or need for kindling, tinder or wood logs. You should only light a Duraflame firelog if you're prepared to enjoy it throughout the entire burn time; while breaking the log up can shorten the burn time, it may also produce unexpected flareups or make the log burn hotter than your fireplace can handle, so the manufacturer recommends against it. If you need to extinguish a burning log, do so thoroughly, to avert the possibility that it may reignite.
Pour water over the Duraflame log in a slow, controlled manner using a metal container. This helps reduce the risk of splashing ash or scattering sparks or burning material. Saturate the entire log from end to end until it has stopped burning.
Break up the Duraflame log using a poker or a stick, looking for any hot spots that may have formed on the inside of the log. Continue dousing the interior surface of the log with water as it's exposed, until you've thoroughly taken the log apart. Scatter the log material as you would scatter coals, and douse any portion that's not already thoroughly wet.
Extinguish any parts of the Duraflame log that can't be put out using water with a dry chemical fire extinguisher, if necessary.