Cisplatin and Flavopiridol in Treating Patients With Advanced Ovarian Epithelial Cancer or Primary Peritoneal Cancer

Inclusion Criteria: * Histologically confirmed ovarian epithelial or primary peritoneal cancer: Advanced disease * Meets at least 1 of the following criteria: * Measurable disease; * Evaluable disease plus CA 125 \>= 2 times post-treatment nadir * Treated with 1, and only 1, prior platin-containing chemotherapy regimen (e.g., paclitaxel or carboplatin-based) for ovarian epithelial or primary peritoneal cancer * Prior treatment with the same regimen at first relapse allowed; * No more than 3 total chemotherapy regimens allowed provided exactly 1 has been platin-containing; * Must also have platin-resistant disease as defined for Group 1; * Rechallenge with a single regimen upon progression after a hiatus from therapy counts as a single regimen * Group 1, meeting 1 of the following criteria: * Patients who relapse during or \< 6 months after completion of post-debulking chemotherapy; * "Platinum sensitive" patients in second relapse after having been treated/rechallenged with their initial regimen upon first relapse * Group 2 (Closed to accrual as of 3/10/06): * Patients who relapse \>= 6 months after completion of post-debulking chemotherapy and are not retreated with the same or a different regimen * No CNS metastases * Performance status: * ECOG 0-2 * Hematopoietic: * Absolute neutrophil count \>= 1,500/mm3; * Platelet count \>= 100,000/mm3; * Hemoglobin \>= 10 g/dL (Note: May be supported with transfusion, epoetin alfa, or darbepoetin alfa) * Hepatic: * AST =\< 2.5 times upper limit of normal (ULN); * Alkaline phosphatase =\< 2.5 times ULN; * Bilirubin =\< 1.5 times ULN * Renal: * Creatinine =\< 1.5 times ULN * Cardiovascular: * No cardiac arrhythmia; * No cardiac failure * Not pregnant or nursing * Negative pregnancy test * More than 3 weeks since prior chemotherapy (6 weeks for nitrosoureas) * More than 3 weeks since prior radiotherapy * Recovered from all prior therapy * Fertile patients must use effective contraception * No other malignancy within the past 5 years except non-melanoma skin cancer or carcinoma in situ of the cervix * No diabetes * No peripheral neuropathy \>= grade 2 * No baseline diarrhea (\>= 4 stools/day) * No uncontrolled infection * No other concurrent uncontrolled serious medical condition * No concurrent routine colony-stimulating factors