Billingsley made the decision after a conversation Sunday with team physician Neal ElAttrache.
"It's the best chance I'll be able to pitch next year," Billingsley said.
Billingsley failed to return from an operation he underwent last year to repair a torn ulnar collateral ligament.
Billingsley said if he rehabilitates his flexor tendon instead of having it surgically repaired, there is significant chance he could reinjure his ulnar collateral ligament. That would require him to undergo a second Tommy John operation.
"The percentages weren't in my favor," Billingsley said. "It was really playing with fire."
Billingsley said he expects to be sidelined for six months.