In the sentence

İyi ayakkabılarını giyin

is the speaker talking about the listener’s certain good pair of shoes which he has seen and whose existance he is sure about? Or is he speaking about good shoes in general, any good shoes that the listener might have in his possession, in which case the accusative marking is here because definiteness is the natural result of the possessive marking. In other words, what is the scope of POSS + ACC here,

İyi [ayakkabılar]ını  giyin

OR [İyi ayakkabılar]ını giyin  ?

Both options are possible.

i think it means wear your good shoes. (not the old, bad quality ones)

My interpretation:

Wear his/her/their good shoes

İyi ayakkabılarını giyin

"-in", which apears to be imperative mood 2nd pl. person suffix, means that speaker is talking to more than one person

his/her/their good shoes means the listeners are told to wear some other person(s)´ shoes

Wear your shoes would be:

iyi ayakkabılarını giy (one listener)

or

iyi ayakkabılarınızı giyin (more than one listener)

Funny. This never occurred to me. Torn apart from its context, the sentence is more ambiguous than I thought.

From my point of view, the ambiguity here occurs because of lack of a comma "," after "iyi".

Because we do not know the context in which this sentence is uttered, we cannot be sure of the meaning. On the hand, in the sentence "İyi ayakkabılarını giyin" does not sound good, so "iyi" cannot be used to mean "good". In everyday turkish, we do not say "iyi (good) ayakkabılarını giyin". Instead of this we say "yeni ayakkabılarını, temiz ayakkabılarını, şu yeni ayakkabılarını" etc.

In my opinion,here "iyi" means "well" but we shall place a comma after it if we want to give the meaning of "well or OK OK..".

"İyi, ayakkabılarını giyin" => "Well(Ok OK), wear your shoes"

"İyi" is more likely an adjective here than an adverb (your interpretion may be possible but less likely I presume).

Second thing "-in" suffix (giy-in) sounds to me to be 2 pl. person imperative suffix rather than a reflexive one.

Ayakkabı giy (this is more likely)

or

Ayakkabı giy-in (this is weird to me if it is reflexive indeed)

How could a reflexive verb take an accusative object (or any object to that point)?

Exactly! But it sounds to me that other native speakers who posted here find it OK.

This reminds me a joke about two scientists who have to spend a night in a room in the house of a poor man. In the middle of the room there is a stove and under the stove are four big stones serving as four long legs that the stove is nearly one meter above the floor. The scientists begin to think to find out the reason of which should be for about the strange position of the stove. One says, " I think it is probably because of obtaining the most effective circulation of heated air", and the other says, "I think it is likely because of obtaining sustainable burning progress." As they disagree with each other they think the best is asking it to the poor man. The poor man says," it is simply because of lack of stovepipe."