You can only be signed into one Klout account at a time within a single browser. Therefore you must sign into your Klout accounts one after the other if using the same browser.
If you are having trouble signing in, please follow these steps:
1. Log out of your first Klout account.
2. Make sure you are signed into the correct account on Twitter.
3. Sign in to Klout again.
If you are still logging into the wrong account, please try clearing your cookies.