I reckon if you used a CR123A lithium battery, you would gain in several ways in return for the extra cost. They are about $2 each in quantity.

Much longer operational life, perhaps even 20+ years. I had a CR123 in a film camera that I stopped using in 2006. When I turned on the camera in 2019 it was still viable. I doubt if an alkaline cell would last 10 years, I have several leak after a few years.

Much simplified circuit, no need for coil since the CR123A is a 3V cell.

Do you find a CR123A cell with a 3Ah rating?  The ones that I find are only 600mAh (https://www.powerstream.com/cr123a-tests.htm).  The lithium CR123A-cells contain less energy than the alkaline AA-cells. 
I agree with you that the circuit could be much simplified using 3V power and that lithium has a lower self discharge.

Edited: Panasonic CR123A (as sold by Mouser) is 1.55Ah (discharged at 100mA).  So yes the energy would come at about the same as the 1.5V AA-cell.

You're taking the Ah rating of lithium at the max discharge rate whereas at a low discharge rate it's more. Also where do you get the 3Ah rating for alkaline cells? https://en.wikipedia.org/wiki/AA_battery gives a range from 1.8 to 2.85. Finally as the lithium cell is 3V, twice the alkaline cell, the energy comes out about the same. Ah is a measure of charge, not energy (Q = I*t), voltage comes into the energy equation.

Hi. I still can´t it work this blinker because looks the cores are agaisnt me. Any idea to find this core (may be yellow)? Thank you.

I don´t have cd4001 then I used TC4001..no problem by change?

Sorry, I mean "4 cores types". Tks

Hi, I tried 4 colors types by now but don't flash, only turn ON and nothing ... my ferrite core is it incorrect (green color)? What  is the key? Thank you by help us.

 There is a comment on your youtube video which shows how to greatly simplify the circuit. Get rid of the whole logic section, and where the jumper is, place a 10-100uf cap and a 100k resistor, and replace the 4.7k resistor with a 1k resistor. With a 100uf cap, it flashes brightly about once per second.

I could not actually get it to work as you designed. Adding the reservoir cap pulled the output below what would light the LED or drive the 4001.

How to wind the coil is not clear. Do you wind once, do the winds need to be tight and not overlap, or does it take multiple layers, does it matter?

Hi! The 2 coils of T1 are wound simultaneously ( 2m wire folded in half = 1m ). When you cut the end after winding the wire, you end up with 2 separate windings. Twisting the wire pair on itself simplifies the winding process. The winding should be as tidy as possible, leaving around 2" of wire at beginning & end for connection. When finished, remove the insulation (enamel) before soldering, and verify with ohmmeter that there are no shorts between coils and to core (ferrite core is conductive). Finally, when building the circuit, polarity of the coils with respect to each other is crucial. If LED does not light when you momentarily short the header pins 1-2, invert the polarity of 1 (only one) of the coils. The best practice, is to build the circuit on a solderless breadboard first, and label the 4 wires.  It´s very difficult to troubleshoot after soldering on the PCBoard.   Greetings!

I have not made this yet, but it sounds like the wire will lap over itself for several windings is this correct?

Yes, the first layer will accept (approximately) 20 turns and the second will fit in the spaces between the turns of the first ( external diameter of  toroidal core ). Regards! 

Thanks, that answered my question.

Nice.  A spiritual successor to the LM3909.

But with 1/10 current ! Greetings!