The correct (official) method is:
Exists: https://api.twitch.tv/kraken/users/barrycarlyon
{
"display_name": "BarryCarlyon",
"_id": 15185913,
"name": "barrycarlyon",
"type": "user",
"bio": "NNNNNEEEEEEEEERRRRRRRRRRRRDDDDDDDDDDDDD",
"created_at": "2010-09-01T17:51:01Z",
"updated_at": "2016-06-13T05:30:07Z",
"logo": "https://static-cdn.jtvnw.net/jtv_user_pictures/barrycarlyon-profile_image-57VGstR8g2yjIFm-300x300.jpg",
"_links": {
"self": "https://api.twitch.tv/kraken/users/barrycarlyon"
}
}
NoExist (at time of writing): https://api.twitch.tv/kraken/users/bobysdfjdhsfjkhdf
{
"error": "Not Found",
"status": 404,
"message": "User 'bobysdfjdhsfjkhdf' does not exist"
}