One of the older style of hand warmer was a metal case with insulation in it that held a burning charcoal stick inside. They usually burned for about 5 hours.
I think you would get the same effect from embers carried in a container full of ash.
(If you have something like this just to carry a fire it seems to me you might be better just packing a lighter with you.)

Another fire carrier is the bark from Douglas Fir. The embers
(coals) seem to burn into is just like punk and smolder away for a long time.
Oh I just reminded me about punk. Punk is the dozey half rotted but dry cedar you find inside some logs. It is another material that will carry an ember for a long time.