COUNTは、個別のサブクエリで実行する必要があります。これでうまくいくはずです。
編集:いくつかの愚かな間違いを修正し、答えにフィドルを含めました。
SELECT DISTINCT E.created,F.flash,C.client
FROM events E
LEFT JOIN (
SELECT created,COUNT(DISTINCT user_id) as flash
FROM events
WHERE event_type LIKE 'Flash C log'
GROUP BY created
) F
ON F.created = E.created
LEFT JOIN (
SELECT Created,COUNT(DISTINCT user_id) as client
FROM events
WHERE event_type LIKE 'Client C log'
GROUP BY created
) C
ON C.created = E.created
WHERE E.created BETWEEN '2016-09-25' AND '2016-09-27'