Based on this instruction, it is only possible to sign message from imported addresses. So, it's impossible to sign message from an address created by blockchain wallet.
To OP: You should extract your seed phrase and import it into another wallet like Electrum. Then you can sign message from that address.
To do so, go to "security center". Scroll down and click on "back up" button. Blockchain wallet will give you a 12-word phrase.
Then install Electrum. Create a new wallet and select "I already have a seed" and enter that 12-word phrase.
In order to sign message using Electrum, click on tool at top of the window and then select "sign/verify message".
Note:
1. Download Electrum only from the official website. (
https://electrum.org/)
2. Don't forget to check BIP39 when entering the phrase.
3. Select Legacy as your address type.