[Flags]

    public enum FlagsEnum

    {

        Day = 1,

        Night = 2

    }

    public class EntityWithEnum

    {

        public int ID { get; set; }

        public FlagsEnum ValidTime { get; set; }

    }

public partial class CodeFirstModel : DbContext

   {

        public CodeFirstModel()

            : base("name=CodeFirstModel")

        {

        }

        public virtual DbSet<EntityWithEnum> EntityWithEnum { get; set; }

}

<connectionStrings>

    <add name="CodeFirstModel" connectionString="data source=(LocalDb)\MSSQLLocalDb;initial catalog=TestDb;integrated security=True;multipleactiveresultsets=True;application name=EntityFramework" providerName="System.Data.SqlClient" />

  </connectionStrings>

static void Main(string[] args)

        {

            //CreateDatabaseIfNotExists

            //DropCreateDatabaseIfModelChanges

            //DropCreateDatabaseAlways

            Database.SetInitializer(new DropCreateDatabaseIfModelChanges<CodeFirstModel>());

            using (var context = new CodeFirstModel())

            {

                context.Database.Initialize(true);

            }

            using(CodeFirstModel db = new CodeFirstModel())

            {

        EntityWithEnum entity = new EntityWithEnum() { ValidTime = FlagsEnum.Day };

                db.EntityWithEnum.Add(entity);

                entity = new EntityWithEnum() { ValidTime = FlagsEnum.Night };

                db.EntityWithEnum.Add(entity);

                entity = new EntityWithEnum() { ValidTime = FlagsEnum.Night| FlagsEnum.Day };

                db.EntityWithEnum.Add(entity);

                db.SaveChanges();

                Console.WriteLine("{0}:\t{1}", entity.ID, entity.ValidTime);

                Console.WriteLine("-------------------");

                var entitys = from e in db.EntityWithEnum

                              where e.ValidTime.HasFlag(FlagsEnum.Day)

                              select e;

                foreach (var item in entitys)

                {

                    Console.WriteLine("{0}:\t{1}", item.ID, item.ValidTime);

                }

            }

            Console.ReadKey(true);

}