If a channel is online it will be under the stream endpoints ex: https://api.twitch.tv/kraken/streams/imaqtpie. That will return something like "created_at": "2016-03-02T12:04:21Z", which is the timestamp for when the stream started
https://github.com/justintv/Twitch-API/blob/master/v3_resources/streams.md#get-streamschannel