Go to the Chrome Web Store and install the SubShift extension .
YouTube limits accounts to a maximum of 75 subscriptions per day for newer or unverified accounts to prevent spam. If your old account has hundreds of subscriptions, an automated tool attempting to add them all instantly will trigger a temporary block.
YouTube Subscriptions Importer: Copy Subscribed Channels to Another YouTube Account
Safety Guide: Never give your Google password to an importer tool. Always use OAuth (the "Sign in with Google" popup) so the tool never sees your password.
Here is how to copy your subscribed channels from one account to another. The Fast Way: Using a Subscription Importer