Bringing Enhanced Treatments and Therapies to ESRD Recipients (BETTER) Kidney Care Act This bill requires the Centers for Medicare & Medicaid Services (CMS) to establish a demonstration program for Medicare beneficiaries with end-stage renal disease (ESRD). Under the program, renal dialysis facilities, kidney disease specialists, physician practices, and other health care practitioners may form an organization that partners with certain health care entities to provide integrated care to beneficiaries with ESRD. Such care must include all covered Medicare benefits as well as transition services for transplantations, palliative care, and hospice. Each organization must have a minimum number or percentage of participating beneficiaries (350 or 60% of beneficiaries served at the organization's facilities) and must also comply with certain fiscal, governance, and quality of care requirements. Additionally, the Government Accountability Office must study certain data that is reported to the CMS regarding pediatric dialysis care, as well as the effects of race-based corrections to a specified kidney function test on referrals of ESRD patients for transplant evaluations.