'No dice' is an American idiom meaning 'no chance'. It's a reference to gambling. So 'It's xx or no dice' means 'It's xx or nothing'. In other words, he's determined to have a blue French horn, and won't consider any other options.
The older Scotch is, the better. He means that he likes Scotch that's, say, 18 or 21 years old - the age at which a person can legally order alcohol.