there is a bug in the article: "red (0) or yellow (1)"  should be yellow (0) or red (1).

Yes, one of your entries helped me to realize my mistake, but as mentioned by Pan Troglodytes, the correlations between different bit streams are still  there
(amongst them correlation between green/blue and slim/fat)

Guys I would like to apologize for a mistake I made in my previews analysis.
I assumed that the private WIF key is random (private/public key pair was generated with a vanitygen like tool without modifications)
so my conclusion was that the "yellow/red", "green/blue" bit stream can not encode a  private key.

Unfortunately my assumption might not nesesery be true,
in fact there only needs to be about length("FLAMEN6")*6bits= 7*6bits = 42bits  random bits in a stream to generate a public key with "1FLAMEN6" prefix,
so not only the "yellow/red", "green/blue" stream may contain a valid private key, but also only the "short/long" stream is enough to create a valid private key with a  "1FLAMEN6" prefix.

Even more, it's probably possible to modify the original vanitygen source code so, that the time it would take to find such a private key is the same as now (on my laptop the estimation is ~5 days). The only change would be to feed vanitygen not with random numbers but with a desired bit pattern + the 42 random bits.

If this is the case in this puzzle, you have to decide for yourself.

Yet another idea:

some leaves are pointing inside chess squares,
what if they indicate the reading order of  flames sides and the direction.
Direction could be imposed by the corner spirals:
if a leaf is pointing  left we go CCW, otherwise we go CW.

https://imgur.com/oLzQaRP

unfortunately I'm not sure if the green color is correct (might also be "inner top" flames)
and if the black color should be taken into account, if not we would have this order (based on leaf marked yellow):
1. inner right CCW
2. outer bottom CW
3. outer top CW
4. inner left CW

hm... yes I've probably missed some numbers

here you go, the full path:
https://imgur.com/gallery/rI1x1

1. follow  leafs
2. follow vine branches (cyan color)
section 1, cyan path, do something with:
3. blue flame  
section 2, cyan path, do something with:
4. white square (probably position)  
5. white queen/bishop
6. blue knight
7. rays (?)
8. white square (probably position)
9. go to  section 3
section 3, yellow path, do something with:
(and so one..., unfortunately we are still in section 1)
(leafs marked green are probably associated with leaf 12)

I would like to share an idea with you, it was probably mentioned before but with no much response,
idea: The branches and leafs show a path to the solution

The beginning of this puzzle is (quote from "The Phoenix and the Turtle" by WILLIAM SHAKESPEARE)
So between them love did shine
That the Turtle saw his right
Flaming in the Phoenix' sight:
Either was the other's mine.  

here is a picture of the idea:
https://imgur.com/gallery/XeMgS

the puzzle is divided into "sections". The path, what to do next, is shown by the branches (sometimes partially obscured by other objects) and leafs.
According to this theory we are in section 1, arrow 1. :-)

some observations: there is the phoenix hair, a brunch "skipping" 1 or 2 branches below, a K (or R or B) and a leaf pointing at the small blue flame

a python (2.7) script for you (not the prettiest but it works):

output:


@RealOnTheMF - I'm impressed!

If someone is interested in symbols:

https://imgur.com/gallery/F22X4

of course they are very subjective

could you give some more info?

speaking of faces:

https://imgur.com/a/uJR0s

image was rotated CCW 90 deg, added to its mirror with 50% alpha,

Yes, that's what I'm suspecting too

I would like to share some statistics I've made,
the conclusion: It is not possible that the "yellow/red", "green/blue" bits (only) encode a  private key
(or at least very unlikely)
(EDIT: see bottom comment)

looking at the distribution of  1's in the "yellow/red", "green/blue" bit streams it looks like the stream is random
we have 78 - 1's in "yellow/red" stream and 77 -1's in "green/blue" stream (nearly 50% of all 152x2 bits)
but if we take only bits if a flame is long:
we get:
P(yellow/red = 1 | long) = 0,6559139785
P(green/blue = 1 | long) = 0,5161290323
this is very strange (assuming the streams are random) but still possible, so let just check every second bit and cut out only bits according to 011011 pattern:

P(yellow/red = 1 | '0 1 1' = 1) = 0,68
P(green/blue = 1 | '0 1 1' = 1) = 0,52
this is very unlikely to happen for a private key, how unlikely?
I've tested 1000 WIF private keys generated with vanitygen in base64, base58 and binary coding,  the highest P(private key = 1| '0 1 1' = 1) was ~0.62

Here are my statistics:
1. average P for a private key generated with vanitygen (1000 samples)
2. P for short/long, yellow/red, green/blue and slim/fat bit streams with cutouts (columns)
https://imgur.com/gallery/JRZFs


in case of 2. we can clearly see there is a correlation between  "short/long" -  "yellow/red" streams and "green/blue" - "slim/fat" streams


EDIT:
In this analysis I assumed that the private key is random, but that is not necessarily true,
in fact we only need 42bits of "randomnes" to generate a public key with a "1FLAMEN6" prefix,
so after all my main conclusion is probably wrong

you mean something like this:

it is a possibility, in some cases the blobs (slim/fat) look like there were corrected.