Once fire is made, spreading it or re-lighting it using embers is easiest. Embers can burn for days if oxygen is restricted and the embers are insulated.

20 years ago, a 5000 year old natural mummy was found carrying an ember bundle and tinder with traces of pyrite (but no flint&pyrite).

http://www.iceman.it/en/mapleleaves

Embers:

On his journey over the Alps the Iceman carried a birch-bark container with him. He used it to store hot embers for starting a fire. He wrapped the embers in freshly picked maple leaves, which served as insulation material. The leaves have retained their chlorophyll down to the present day.

Fire-starting:

To make a fire, prehistoric people for thousands of years used a “fire-lighting kit” which contained a piece of flint, a piece of pyrite, and tinder. The Iceman, for example, carried a piece of dry tinder fungus for starting fires. Fine pyrite particles were found on the fungus, proving that Ötzi used pyrite to produce sparks, although no pieces of pyrite were found on his person. Steel (photo) replaced pyrite for producing sparks in the Middle Ages.

Here is a short modern survivalist post about carrying embers: http://survivor-magazine.com/carrying-fire/

edit: explain a little more about embers