The Streak API is tied to your Streak account. Simply login into Gmail and make sure Streak is enabled. Click on the Streak dropdown in the top right navigation bar of Gmail and find the "Integrations" button.
Click on the button for Developers.
This will open a window where you can view existing integrations and create new API keys. Treat your API key like a password, as it has full access to your account. If you feel it has been compromised, you can always delete it and create a new one from the dialog.
Keep your API key(s) secret.