Best way is to use a coin mixer.
There are many people using mixers these days to stay anonymous.
Mix the coins...
Bitmixer.io small fees excellent service!
Why even go through the hassle of paying to use a coinmixer for this when you can just send the payment to any bitcoin casino of your choice and then withdraw it? If you want further privacy find a site that allows tor and create a new account.
You don't know what logs are being kept by those sites.... the fee of withdrawing is allmost similar to the fee of bitmixer.io