Kickham was outrighted to Triple-A Oklahoma City after clearing waivers Thursday, Eric Stephen of SBNation.com reports.
Kickham was designated for assignment Monday.
Kickham had his contract selected by the Dodgers on Sunday, Jorge Castillo of the Los Angeles Times reports.
The Dodgers reassigned Kickham to their minor-league camp Tuesday, Juan Toribio of MLB.com reports.
Kickham signed with the Dodgers as a non-roster invitee Tuesday, Eric Stephen of SBNation.com reports.
Kickham became a free agent Monday after being outrighted off Boston's big-league roster, Christopher Smith of The Springfield Republican reports.
Kickham is expected to move to the bullpen after manager Ron Roenicke didn't name him as a starter for any of the Red Sox's final five games of the season, Bill Koch of The Providence Journal reports.
Kickham (1-1) allowed six runs on seven hits (two home runs) while striking out three across 2.2 innings Wednesday as he took the loss against the Marlins.
Kickham will start Wednesday against the Marlins.
Kickham allowed two earned runs on three hits and one walk while striking out eight across four innings Thursday against the Rays. He did not factor into the decision.