How can I safely charge 3 lithium 18650 batteries to use in one pack?
Read my just posted answer to this question. While not identical it covers aspects which will answer some of your questions.

3 x 18650 LiIons (or any 3 LiIons) will have a fully charged voltage of 3 x 4.2V = 12.6V and a fully discharged voltage of ABOUT 3 x 3 = 9V. How low low goes is up to you. Too low and battery dies.

Read my answer above re balancing. It is not NECESSARY as long as you are CERTAIN that no cell is ever deep discharged AND if charging in series, as long as no cell is in constant voltage tail off mode while you are attempting to inject full constant current at 1C. 'Attempting to" period may be short. 

IF you charge this off the bike and if all 3 cells are isolated from the world (but connected to each other) then my answers above re charging one at a time apply. You can charge 3 at a time with 3 chargers ** as long as** all charger outputs are truly isolated.

An easy way to get 12V is to use one of the many many available switch mode power supplies. You can get 1 or 2 or 3 cell LiIon to 12V capable supplies.

An 18650 LiIon cell is has a capacity of about 2000 mAH x 3.6V nominal =~~ 7 Watt hours.  IF your flasher worked at 1 Watt average and was anything like serious it would blow following motorists off the road. Depends on design. 1 Watt at 10% duty cycle = 10 Watts when one. 1 Watt at 1% duty cycle = 100 Watts when on. Properly collimated a 1 att red LED willl do a very very very very good job. So a single 18650 cell with inverter of say 7% efficient (low) will run for 7 Wh/1 Watt x 70% = 5 hours. Ample for most people. 



ADDED:  


OK, so some clarifying questions.
1) how can I be certain that no cell is ever "deep discharged"?   


No cell ever under 3 Volt.  


Monitor voltage and prevent this happening   


OR  


Never discharge beyond known capacity to ensure this is true.


Murphy says you will fail if you take the 2nd choice.


2) if I'm using a COTS charger (and charging each cell separately), what do you mean by the charger outputs must be truly isolated? If I'm using a physically separate charger for each cell,


If the cells are not connected in any way this is irrelevant.
 This is an issue only if the cells are connected as in a battery holder. 

Outputs are fully isolated from the charger input.
 If you operate 2 chargers from mains simultaneously you must get no sensible voltage readings when measuring from eg V+ out of one to V+ out of other.
 If you plav a resistor from V+ out of oneto Ground out of th eother no current flows.
 Well under 1 mA would be acceptable.
I'd expect good isolation. What is to be avoided is having ground out hard connected to ground pin in.

3 truly isolated chargers will work happily on 3 cells in series if there is no closed current path apart from the cell interconnections.


will it be safe if when they're done charging separately I put all three cells back into the same system together


Yes.