For everyone stating that there is no question (in either direction), please state who you have yadin yadin smicha from. If you want to say that you personally have strong ethical feelings one way or another on this, that's one thing. But if you want to say it's not even a question halachically, you should probably explain why.
I have no idea what the actual psak would be, and I think it's a very interesting shaila. Personally, I would probably change the password but not use the account at all. Tell the Jewish broker to inform the non-Jewish broker that the points are still there and he (the non-Jewish broker) should contact you for your info if he's ready to use the miles, or at least give you a reasonable timeframe by which they'll be used.