A REST API will be developed to accept username and password and do
the authentication. The HTTP method to be used is POST so that there
is no caching. Also, there will be SSL for security at the time of
transit
This is the way most do it, so you're good here.
At the time of authentication, two JWTs will be created - access token
and refresh token. Refresh token will have longer validity. Both the
tokens will be written in cookies so that they are sent in every
subsequent requests
Storing the tokens in cookies I not dangerous in itself, but if you somehow get you JWT module on your server to read them from there you vulnerable to CSRF attacks where any webpage can trigger a users browser to send a form + you sites cookie to your server unless you use CSRF tokens. So generally they are stored in localStorage and "manually" added to request headers every time.
On every REST API call, the tokens will be retrieved from the HTTP
header. If the access token is not expired, check the privileges of
the user and allow access accordingly. If the access token is expired
but the refresh token is valid, recreate new access token and refresh
token with new expiry dates (do all necessary checks to ensure that
the user rights to authenticate are not revoked) and sent back through
Cookies
Apart from the cookie dangers, it seems safe.
Provide a logout REST API that will reset the cookie and hence
subsequent API calls will be rejected until login is done.
You don't even need to make an API call, you can simply just purge the cookies or the localStorage object and make sure your client doesn't break on missing tokens.
The standard for the express-jwt module expects the tokens to be in its own "Authorization: Bearer [Token]" header, which I would strongly recommend over cookies. The localStorage API is available all the way back to IE8 so you should be good.
Edit:
First, it's important to know the difference between XSS and CSRF attacks since they're often believed to be the same thing.
XSS is when users get unsafe JS running on your domain in other users browsers when that happens neither JWT in localStorage or sessions and JWT in cookies are safe. With httpOnly flag on cookies, you can't directly access them, but the browser will still send them with AJAX requests to your server. If this happens you generally out of luck. To prevent this, make sure to escape all user input if it's sent to the browser.
If you load 3rd party JS with script tags or iframes this might compromise localStorage unless you are careful, but I haven't worked enough with this to help you here.
CSRF is only when other domains are trying to send normal HTML forms to your server by getting the browser to send cookies automatically. Frameworks prevent this by inserting unique random strings as hidden fields and checking them again when it's submitted. JWT's in localStorage is safe from this since each domain gets its own separate localStorage area.
But ultimately all this depends on if your service will be using one single domain, in which case httpOnly cookies will be plenty secure and easier to set up, but if you wanna spread your service out on multiple domains like api.domain.com + app.domain.com or add a native app you're forced to store you're JWTs in localStorage or some other native storage area.
Hope this helps!