It looks like a duplicate of old issue https://github.com/localstack/localstack/issues/78
But now it's reproducible for me with the latest version of LocalStack. 
aws_stack.create_kinesis_stream(self.TEST_STREAM_KINESIS_API_GW)
        
        result = self.connect_api_gateway_to_kinesis('test_gateway1', self.TEST_STREAM_KINESIS_API_GW)
        
        test_data = {'records': [
            {'data': '{"foo": "bar1"}'},
            {'data': '{"foo": "bar2"}'},
            {'data': '{"foo": "bar3"}'}
        ]}
        url = INBOUND_GATEWAY_URL_PATTERN.format(
            api_id=result['id'],
            stage_name=self.TEST_STAGE_NAME,
            path=self.API_PATH_DATA_INBOUND
        )
        
        result = requests.get(url)
        result = json.loads(to_str(result.content))
        self.assertIn('StreamNames', result)
        
        result = requests.post(url, data=json.dumps(test_data))
        result = json.loads(to_str(result.content))
        self.assertEqual(result['FailedRecordCount'], 0)
        self.assertEqual(len(result['Records']), len(test_data['records']))
        
        kinesis = aws_stack.connect_to_service('kinesis')
        kinesis.delete_stream(StreamName=self.TEST_STREAM_KINESIS_API_GW)