Reddit provides a way to streamline this for you - I use old.reddit.com so it might not be the same in the new UI so YMMV on the specifics.
While logged in, click the subreddits dropdown and click the "Edit Subscriptions" link, it takes you to https://www.reddit.com/subreddits/ - on the right side is "multireddit of your subscriptions" -- this is a URL string of all your subreddits, just save the URL. When you make a new account, click the URL again and subscribe to them on your new account.
While logged in, click the subreddits dropdown and click the "Edit Subscriptions" link, it takes you to https://www.reddit.com/subreddits/ - on the right side is "multireddit of your subscriptions" -- this is a URL string of all your subreddits, just save the URL. When you make a new account, click the URL again and subscribe to them on your new account.