Eventbridge to Kinesis data streams cross account

EventBridge does not currently support sending events directly to a Kinesis data stream in a different account. The only cross-account resource supported as a target is another EventBridge bus. In your scenario, the simplest solution will likely be to send the event from EventBridge bus (Account A) to a new EventBridge bus (Account B), and then from EventBridge bus (Account B) to the Kinesis data stream (Account B). Additional guidance on sending events across accounts can be found here: https://docs.aws.amazon.com/eventbridge/latest/userguide/eb-cross-account.html