Families Learning and Understanding English Together Act of 2021 or the FLUENT Act This bill authorizes the Department of Education (ED) to establish a grant program to improve the literacy and English skills of English language learners. Specifically, ED may award grants to providers of family literacy services to provide these services to families with English language learners. These services may only be provided to a family in which each caregiver is 16 years of age or older and at least one child is under the age of 8. Further, ED must make grants to or enter into contracts with at least two national organizations with expertise in providing family literacy services to English language learners. These national organizations must provide grantees with technical assistance and training.