How do I get the AccountId as a variable in a serverless.yml file?

There's a handy serverless plugin https://www.npmjs.com/package/serverless-pseudo-parameters that adds the ability to reference aws parameters such as region and account id that i've just started using to much success.

This is now supported natively in Serverless Framework.

functions example

  functions:
    hello:
      handler: my-function.handler
      environment:
        var: !Sub arn:aws:logs:${AWS::Region}:${AWS::AccountId}:log-group:/aws/lambda/*:*:*'

iam role example

  iam:
    role:
      statements:
        - Effect: Allow
          Action:
            - dynamodb:*
          Resource: !Sub arn:aws:dynamodb:${AWS::Region}:${AWS::AccountId}:table/${AWS::StackName}-*

See Pseudo Parameters Reference for the official docs.