Irinotecan Hydrochloride With or Without Alvocidib in Treating Patients With Advanced Stomach or Gastroesophageal Junction Cancer That Cannot Be Removed By Surgery

Inclusion Criteria: * The patient must have pathologically confirmed carcinoma of the stomach or GEJ (Siewert's type I, II, or III); confirmation will be performed locally at each participating institution * The patient must have advanced disease not amenable to surgical resection * Patients must have disease that can be evaluated radiographically; this may be measurable disease or non-measurable disease; measurable disease is defined as that which can be measured in at least one dimension as \> 20 mm with conventional techniques, or \> 10 mm by high resolution imaging; disease that is identified on radiology studies, but does not meet the criteria for measurable disease, is considered non-measurable * The patient must have received one prior chemotherapy regimen for his or her unresectable or metastatic disease; this does not include therapy administered in the adjuvant or neoadjuvant setting * At least 2 weeks must have elapsed since the patient received prior chemotherapy, anti-angiogenic therapy, or other targeted therapy; 2 weeks since prior radiation therapy; or, 4 weeks if the last regimen included carmustine (BCNU) or mitomycin C * The patient must have a Karnofsky performance status of \>= 60 * Serum creatinine =\< 2 mg/dl * Total serum bilirubin =\< 2 mg/dl * If the patient has Gilbert's disease and has a serum bilirubin greater than 2.0 mg/dl, the case must be discussed with the principal investigator; such a patient may be considered eligible on a case-by-case basis * Serum aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/ alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 times the upper limit of normal, or * Serum AST (SGOT)/ ALT (SGPT) =\< 5 times the upper limit of normal in case of liver metastases * White blood cell (WBC) \>= 3000/mm\^3 * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelets \>= 75,000/mm\^3 * The patient must have available tumor tissue for assessment of p53 status by immunohistochemistry (IHC) (=\< 20% cutoff for positivity) * Tumor must be p53 wild type as defined as =\< %20 nuclear staining on immunohistochemistry * Women of child-bearing potential and sexually active males must be counseled to use an accepted and effective method of contraception (including intrauterine device \[IUD\], oral contraceptives, or barrier devices) while on treatment and for at least two months after their last treatment on this study; woman also must agree to refrain from nursing during the duration of this study and for at least two months after their last treatment on this study; women of child-bearing potential must have a negative serum pregnancy test to be eligible for this study * The patient must have the mental capacity to understand the nature of this study and provide informed consent to participate Exclusion Criteria: * The patient may not have previously received irinotecan or flavopiridol * The patient may not be receiving any other investigational agents * The patient may not have any ongoing grade 2 or greater toxicity from a prior treatment * The patient may not have an ongoing uncontrolled illness including, but not limited to active infection, symptomatic congestive heart failure, myocardial infarction in the past 6 months, or new cardiac arrhythmia in the past 6 months * Patients with a diagnosis of active human immunodeficiency virus (HIV) infection, on anti-retroviral therapy, or with a cluster of differentiation 4 (CD4) count less than 200 are ineligible due to potential interactions between irinotecan, flavopiridol, and anti-retroviral medications as well as possible immunosuppressive activity of the study treatment