Can I say that heat from the flame is conducted to the air, then the air heats up, and conducts heat to my hand via conduction? ?

there is conduction involved (manifested primarily through convection: the air heats by conduction then moves and heats elsewhere by conduction), but there is also radiation.  How much is due to which process depends on location (distance from source and position relative to flame).

Conduction is always occurring when there is a temperature disparity.  It is just slow and localized (for heat to transfer over any significant distance in any reasonable time frame, convection has to occur).  Radiant heating requires a medium that is transparent to the radiant energy (infrared energy dominates from most fires although some energy is spread across the spectrum).  A lot of heat that you feel from a campfire is radiant heat.  Most of the conducted and convected heat goes upward, so the person tends to actually get caught in a draft of air flowing from away toward the fire.  The physical setup matters a lot, though.

Fame to Air: convention & radiation

Air to hand: convention & radiation