• Patients must have a histologically confirmed diagnosis of metastatic invasive triple negative breast cancer. Patients with clinical and/or radiologic suspicion of metastatic TNBC can be consented prior to this confirmation.

• Estrogen receptor (ER) and progesterone receptor (PR) less than Allred score of 3 OR less than 1% positive staining cells in the invasive component of the tumor.

• HER2 negative by fluorescence in situ hybridization (FISH) or immunohistochemistry (IHC) staining 0 or 1+.

• PD-L1 negative by a Clinical Laboratory Improvement Act (CLIA) approved laboratory using compatible assays appropriate for treatment decisions.

• Patients may have measurable or evaluable disease.

• Patients must be willing to undergo biopsy and have accessible lesions for a new biopsy, or they must have sufficient tissue available from a biopsy performed for standard of care (specifications below). If patient does not have enough archived tissue available, a new biopsy is required. A tumor specimen obtained from relapsed metastatic or locally advanced disease (if applicable) must be submitted. Acceptable samples include core needle biopsies for deep tumor tissue (minimum 4 cores) or excisional, incisional, punch, or forceps biopsies for cutaneous, subcutaneous, or mucosal lesions. Formalin-fixed, paraffin-embedded (FFPE) tumor specimens in paraffin blocks are preferred; FFPE tumor tissue sections on slides may be provided if sufficient material (15 x 10μ- unstained) is available. Fine-needle aspiration, brushing, cell pellet from pleural effusion, bone metastases, and lavage samples are not acceptable.

• No prior therapy for metastatic TNBC. Patients who have received taxane-based adjuvant therapy are required to have a disease-free interval of at least 12 months after completion of taxane therapy.

• Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of durvalumab (MEDI4736) and tremelimumab in combination with neoantigen vaccine in patients \< 18 years of age, children are excluded from this study, but will be eligible for future pediatric trials

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 60%).

• Body weight \> 30 kg.

• Must have a life expectancy of at least 12 weeks.

• Absolute neutrophil count \>= 1,500/mcL.

• Platelets \>= 100,000/mcL.

• Hemoglobin \>= 9.0 g/dL.

• Serum bilirubin =\< 1.5 x institutional upper limit of normal.

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal unless liver metastases are present, in which case it must be =\< 5 x institutional upper limit of normal.

• Calculated creatinine clearance \> 40 mL/min by the Cockcroft-Gault formula or by 24-hour urine collection for determination of creatinine clearance.

• Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply:

‣ Women \< 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy).

⁃ Women \>= 50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \> 1 year ago, had chemotherapy-induced menopause with last menses \> 1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy or hysterectomy).

• The effects of durvalumab (MEDI4736) and tremelimumab and neoantigen vaccine on the developing human fetus are unknown. For this reason and because these agents may be teratogenic, women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and through 180 days after completion of durvalumab (MEDI4736) and tremelimumab. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

• Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up.

• Human immunodeficiency virus (HIV)-positive patients are eligible provided they have a negative viral load, CD4 count \> 250, and are on a stable antiretroviral regimen.

• Ability to understand and the willingness to sign a written informed consent document. Patients with impaired decision-making capacity who have a close caregiver or legal guardian are also eligible with the consent of the caregiver/guardian.