The cookie value is quoted by the Werkzeug library to be safe for use in Cookie headers; this includes quoting any commas, semicolons, double quotes and backslashes:

cookie_quoting_map = {
    b',' : b'\\054',
    b';' : b'\\073',
    b'"' : b'\\"',
    b'\\' : b'\\\\',
}

Anything else outside of letters, digits and the characters !#%&'~_`><@,:/$*+-.^|)(?}{= is encoded to an octal codepoint as well. If there are any escaped values in the cookie, the whole cookie is also surrounded by double quotes.

If you need access to the cookie value in JavaScript, you'll have to decode this again. Values that start with a slash and 3 digits are octal values; a String.replace() call should do:

function decode_flask_cookie(val) {
    if (val.indexOf('\\') === -1) {
        return val;  // not encoded
    }
    val = val.slice(1, -1).replace(/\\"/g, '"');
    val = val.replace(/\\(\d{3})/g, function(match, octal) { 
        return String.fromCharCode(parseInt(octal, 8));
    });
    return val.replace(/\\\\/g, '\\');
}

Demo:

> // recreate properly escaped value
> var cookie = "\"{\\\"message\\\": \\\"hello\\\"\\054 \\\"type\\\": \\\"success\\\"}\""
> cookie
""{\"message\": \"hello\"\054 \"type\": \"success\"}""
> decode_flask_cookie(cookie)
"{"message": "hello", "type": "success"}"
> JSON.parse(decode_flask_cookie(cookie))
Object {message: "hello", type: "success"}

I ended up solving my own issue after finding how flask does this in the source. I was in a hurry at work so did not have time to better explain.

from flask import Flask, session
from flask.sessions import SecureCookieSessionInterface
    
app = Flask("example")
app.secret_key = "Tom Izzo 4 President"

# 1. this is what I was looking for
session_serializer = SecureCookieSessionInterface() \
                        .get_signing_serializer(app)
    
@app.route("/")
def test():
    session["lst"] = ["a", "b", "c", "d"]

    # 2. and this is how I needed to use it
    session_cookie = session_serializer.dumps(dict(session))

The variable session_cookie above is a valid cookie value for a session using the given secret_key. With this I am able to forward a request to another flask server that uses the secret_key.