Sotirios Zormpas I found a clear explanation on this site about Base64: https://base64.guru/learn/base64-algorithm/encode. 
With that I was able to recreate encoding and decoding functions in Ninox script (see attached file). 

To do this, we need ASCII manipulation functions (string operations): 

- decToHexa: converts an 8-bit decimal number into a hexadecimal value,

- chr : returns a character from an ASCII code (number),

- ord: returns the ASCII code of the first character in the string passed as a parameter. 

These functions are then used by encodeBase64 and decodeBase64.

"----------------------------
String operations
-----------------------------";
function decToHexa(value : number) do
    var hexa := ["0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", "F"];
    var u := value % 16;
    var d := floor(value / 16);
    item(hexa, d) + item(hexa, u)
end;
function chr(ascii : number) do
    urlDecode("%" + decToHexa(ascii))
end;
function ord(t : text) do
    var ascii := urlDecode("%00%01%02%03%04%05%06%07%08%09%0A%0B%0C%0D%0E%0F%10%11%12%13%14%15%16%17%18%19%1A%1B%1C%1D%1E%1F%20!%22#$%25&'()*+,-./0123456789:;%3C=%3E?@ABCDEFGHIJKLMNOPQRSTUVWXYZ%5B%5C%5D%5E_%60abcdefghijklmnopqrstuvwxyz%7B%7C%7D~%7F%C2%80%C2%81%C2%82%C2%83%C2%84%C2%85%C2%86%C2%87%C2%88%C2%89%C2%8A%C2%8B%C2%8C%C2%8D%C2%8E%C2%8F%C2%90%C2%91%C2%92%C2%93%C2%94%C2%95%C2%96%C2%97%C2%98%C2%99%C2%9A%C2%9B%C2%9C%C2%9D%C2%9E%C2%9F%C2%A0%C2%A1%C2%A2%C2%A3%C2%A4%C2%A5%C2%A6%C2%A7%C2%A8%C2%A9%C2%AA%C2%AB%C2%AC%C2%AD%C2%AE%C2%AF%C2%B0%C2%B1%C2%B2%C2%B3%C2%B4%C2%B5%C2%B6%C2%B7%C2%B8%C2%B9%C2%BA%C2%BB%C2%BC%C2%BD%C2%BE%C2%BF%C3%80%C3%81%C3%82%C3%83%C3%84%C3%85%C3%86%C3%87%C3%88%C3%89%C3%8A%C3%8B%C3%8C%C3%8D%C3%8E%C3%8F%C3%90%C3%91%C3%92%C3%93%C3%94%C3%95%C3%96%C3%97%C3%98%C3%99%C3%9A%C3%9B%C3%9C%C3%9D%C3%9E%C3%9F%C3%A0%C3%A1%C3%A2%C3%A3%C3%A4%C3%A5%C3%A6%C3%A7%C3%A8%C3%A9%C3%AA%C3%AB%C3%AC%C3%AD%C3%AE%C3%AF%C3%B0%C3%B1%C3%B2%C3%B3%C3%B4%C3%B5%C3%B6%C3%B7%C3%B8%C3%B9%C3%BA%C3%BB%C3%BC%C3%BD%C3%BE%C3%BF");
    index(ascii, substr(t, 0, 1))
end;
"----------------------------
base64 functions
-----------------------------";
function encodeBase64(value : text) do
    var base64Chars := "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
    var base64Result := "";
    var binaryString := value;
    " Convertir la chaîne en une chaîne binaire";
    var b := [{}][false];
    while length(binaryString) > 0 do
        var val := 0;
        var s := slice(binaryString, 0, 3);
        binaryString := slice(binaryString, 3, length(binaryString));
        for i in range(0, 3) do
            val := val * 256 + ord(text(item(s, i)))
        end;
        var res := "";
        for i in range(0, 4) do
            var numCar := val % 64;
            var car := item(base64Chars, numCar);
            res := car + res;
            val := floor(val / 64)
        end;
        var nbCode := ceil(length(s) * 8 / 6);
        res := slice(res, 0, nbCode);
        for i in range(nbCode, 4) do
            res := res + "="
        end;
        base64Result := base64Result + res
    end
;
    base64Result
end;
function decodeBase64(base64 : text) do
    var base64Chars := "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
    var base64String := base64;
    var stringResult := "";
    while length(base64String) > 0 do
        var s := slice(base64String, 0, 4);
        base64String := slice(base64String, 4, length(base64String));
        var val := 0;
        for i in range(0, 4) do
            val := val * 64;
            if item(s, i) != "=" then
                val := val + index(base64Chars, text(item(s, i)))
            end;
        end;
        var res := "";
        var v := 0;
        for i in range(3, 0) do
            v := val % 256;
            if v > 0 then
                res := chr(val % 256) + res
            end;
            val := floor(val / 256);
        end;
        stringResult := stringResult + res
    end
;
    stringResult
end

Encoding and decoding are limited to 8bit character strings. As with the btoa() JavaScript function (https://developer.mozilla.org/fr/docs/Web/API/btoa), if you are using 16bit unicode characters, such as emotionne, the conversion will not work (and no error will be generated). For strings containing unicode, you must first convert them using encodeURI. Similarly, after decoding, you must use decodeURI to recover the original string.