A Study to Find the Highest Dose of Imetelstat in Combination With Fludarabine and Cytarabine for Patients With AML, MDS or JMML That Has Come Back or Does Not Respond to Therapy

Inclusion Criteria: * Patients must be ≥ 1 year and ≤ 18 years of age at the time of study enrollment * Patients, with or without down syndrome (DS), and with acute myeloid leukemia, therapy-related AML, MDS or JMML and meet one of the following: * Second or greater relapse or refractory AML, including isolated extramedullary disease (EMD), but excluding isolated central nervous system (CNS) or isolated testicular relapse * First or greater relapse of MDS * First or greater relapse of JMML * For flow cytometry, it's strongly recommended to enroll onto APAL2020SC or to send samples to Hematologics, Inc. Otherwise, assessments must be performed at a College of American Pathologists (CAP)/Clinical Laboratory Improvement Act (CLIA) certified lab that has expertise in AML. * For fluorescence in situ hybridization (FISH)/Karyotype, samples must be sent to a Children's Oncology Group (COG)-approved Cytogenetics Lab * Bone marrow relapse AML: (patients must meet one of the following criteria to be defined as having relapsed disease) * A single bone marrow sample showing ≥ 5% leukemic blasts by flow cytometry, fluorescence in situ hybridization (FISH) testing, or other molecular method * A single bone marrow with at least two tests showing ≥ 1% leukemic blasts; examples of tests include: * Flow cytometry showing ≥ 1% leukemic blasts by multidimensional flow cytometry (MDF) * Karyotypic abnormality with at least one metaphase similar or identical to diagnosis * FISH abnormality identical to one present at diagnosis * Polymerase chain reaction (PCR) or next generation sequencing (NGS)-based demonstration of leukemogenic lesion identical to diagnosis and ≥ 1% * In cases where a bone marrow aspirate cannot be obtained because of extensive fibrosis, blast count can be obtained from touch imprints or estimated from an adequate bone marrow core biopsy. A complete blood count documenting the presence of at least 1,000/uL (i.e., a white blood cell \[WBC\] count ≥ 10,000/uL with ≥ 10% blasts or a WBC count of ≥ 5,000/uL with ≥ 20% blasts) circulating leukemic cells (blasts) can also be used if a bone marrow aspirate or biopsy cannot be performed * Extramedullary relapse: Biopsy proven extramedullary disease after documented complete remission * Refractory disease AML: Following a re-induction cycle after a second relapse, or refractory to two reinduction attempts after either primary induction failure or first relapse with: * A single bone marrow sample showing ≥ 5% leukemic blasts by flow cytometry, fluorescence in situ hybridization (FISH) testing, or other molecular method * A single bone marrow with at least two tests showing ≥ 1% leukemic blasts: examples of tests include: * Flow cytometry showing ≥ 1% leukemic blasts by multidimensional flow cytometry (MDF) * Karyotypic abnormality with at least one metaphase similar or identical to diagnosis. * FISH abnormality identical to one present at diagnosis * Polymerase chain reaction (PCR) or next generation sequencing (NGS)-based demonstration of leukemogenic lesion identical to diagnosis and ≥ 1% * In cases where a bone marrow aspirate cannot be obtained because of extensive fibrosis, blast count can be obtained from touch imprints or estimated from an adequate bone marrow core biopsy. A complete blood count documenting the presence of at least 1,000/uL (i.e., a WBC count ≥ 10,000/uL with ≥ 10% blasts or a WBC count of ≥ 5,000/uL with ≥ 20% blasts) circulating leukemic cells (blasts) can also be used if a bone marrow aspirate or biopsy cannot be performed * Extramedullary refractory disease: * Biopsy proven persistent extramedullary disease * In cases where a bone marrow aspirate cannot be obtained because of extensive fibrosis, blast count can be obtained from touch imprints or estimated from an adequate bone marrow core biopsy. A complete blood count documenting the presence of at least 1,000/ µL (i.e., a WBC count ≥ 10,000/μL with ≥ 10% blasts or a WBC count of ≥ 5,000/μL with ≥ 20% blasts) circulating leukemic cells (blasts) can also be used if a bone marrow aspirate or biopsy cannot be performed * Central nervous system disease: Patients with relapsed or refractory disease with central nervous system (CNS) 1 and CNS 2 status are eligible * MDS: Bone marrow relapse: (patients must meet one of the following criteria to be defined as having relapsed disease) * A single bone marrow sample showing ≥ 5% leukemic blasts by flow cytometry, FISH, or other molecular method * A single bone marrow with at least two tests showing ≥ 1% leukemic blasts; examples of tests include: * Flow cytometry showing ≥ 1% leukemic blasts by multidimensional flow cytometry (MDF) * Karyotypic abnormality with at least one metaphase similar or identical to diagnosis * FISH abnormality identical to one present at diagnosis * Polymerase chain reaction (PCR) or next generation sequencing (NGS)-based demonstration of MDS associated lesion identical to diagnosis and ≥ 1% * In cases where a bone marrow aspirate cannot be obtained because of extensive fibrosis, blast count can be obtained from touch imprints or estimated from an adequate bone marrow core biopsy * JMML: Diagnosis: Patients must have had histologic verification of juvenile myelomonocytic leukemia (JMML) at original diagnosis and currently have relapsed or refractory disease. The diagnosis is made based on the following criteria * JMML category 1 (all of the following): * Splenomegaly * \> 1000 (1 x 10\^9 /uL) circulating monocytes * \< 20% Blasts in the bone marrow or peripheral blood * Absence of the t(9;22) or BCR/ABL fusion gene * The diagnostic criteria must include all features in category 1 and either (i) one of the features in category 2 or (ii) two features from category 3 to make the diagnosis * JMML category 2 (at least one of the following if at least two category 3 criteria are not present): * So