I was trying to use const array for append function, but i seems it can't be seen there.
I tried to add arguments to function nextAppend, but it has no use.
function displayCombat()
{
    $.ajax({
        url: "../php/players_fight.php",
        cache: false,
        success: function (json) {
            const battleLog = JSON.parse(json);
            for (i = 1; i < battleLog.length; i++)
            {
                $('#cWin').append('').delay(200).queue(function nextAppend()
                {
                    $(this).append(battleLog[i]);
                    nextAppend();
                });
            }
        }
    });
    return false;
}
In result nothing is appearing on log div. "Duplicated" solution does not work...
