So your main concerns are, of course, light and smoke. Light is much more visible at night, smoke is more visible during the day (caveat: smoke stands out less against a night sky than day, but a sufficiently think plume will still be quite visible against star or moonlight.) Your best method/time to try to cook will depend on which of those factors you are better able to control. Smoke is reduced primarily by having better quality fuel - the more readily and completely your fuel burns, the less it will smoke. That usually takes time and preparation - making charcoal, storing and drying out firewood, rendering flammable oils, whatever - which your character probably doesn't have the luxury of doing, nor the individual carrying capacity to try to lug around dozens of pounds worth of ready to use fuel.. so, assuming they are needing to rely largely on fallen/found wood (because cutting down live wood both produces very poor quality fuel and leaves really obvious signs that somebody is harvesting wood) then they can't do much about the smoke. That suggests they're probably doing what they can to cook at night, and will be doing their best to manage the amount of light they produce and the directions from which that light can be easily seen.
So.. make only the amount of fire you absolutely strictly need (this also reduces the amount of smoke you make and the trackable traces of where you were - ashes, spots where you burnt away grass/left burn marks on stones, etc, so this is probably the number one thing in general.) Make your fire in a place where visibility is reduced. If possible, construct or hang barriers to reduce the number of directions your firelight can be easily seen from. Helps if you know which direction(s) your possible pursuers may be searching from. After your fire is done do your best to remove signs of having had a fire there, in case your pursuers find one of your old campsites but not you.