Depends on where you are bugging to and how long you plan on staying. Take as many lights and batteries as you know you need to get to where you are going
2 should be plenty. Since you'll be carrying this bag, you have to ask yourself, "Is there something I need in this bag more than I need a 3rd flashlight?" The answer is almost certainly, "yes".
I`d have 3, 2 in my bag one on me at all times, always take an AA and AAA because you can get the batts for these anywhere, and an Anduril light with built in charging (don`t forget the leads) so you can do sublumen to daylight.
One flashlight (Fenix LD25) and one headlamp (ThruNite TH20). 12 AA Eneloops in small plastic cases and a Powerfilm foldable solar charger (the one WITHOUT the USB). All up that weighs 1pd 6.4oz and should take care of your personal lighting needs for the first few years of the crisis.
Sweetie, I gotta ask, what exactly is it you`re running from? because it sounds like you`re going to be quite misserable for however long it takes you to return home again. You certainly won`t be able to have any fires to keep you warm (and it`s mid winter). have you considered bugging IN instead? or if it`s someone`s after you, then just pull a load of cash out the bank, buy a burner (leave your mobile phone at home) and skip state and lay low in a motel somewhere.
This does all sound rather extreme to me, are you Sure it`s the right thing to do and you have no alternatives?
This. In any enthusiast forum that touches on survival there is a tendency to fixate on the forum's central subject - flashlights, knives, guns, radios, first aid, whatnot. The flashlights you'll almost certainly want will be compact/lightweight, durable/reliable, offer long runtime, and have some possibility of refueling or recharging - in that general order. In an actual bug-out situation you will almost surely be limiting your usage to brief short-range usage for close-up tasks and navigation. Most of us can see surprisingly well at night without a flashlight so long as there is some ambient light - in open areas generally further and with a wider field of view.
Otherwise, your focus is should be on survival basics - water, food, protection from the elements, shelter - and items that support those needs in addition to mobility and signaling capability.