Hi Jim,
For me this seems to work, the problem may be that you need to put a L on the end of 0x04…00L,.  Also, if you want 64 values you should be able to use ulong as the enum type.
Try this for example:
        public enum FlaggedEnum64 : ulong
        {
            Bit01 = 0x0000_0000_0000_0001L,
            Bit02 = 0x0000_0000_0000_0002L,
            Bit03 = 0x0000_0000_0000_0004L,
            Bit04 = 0x0000_0000_0000_0008L,
            Bit05 = 0x0000_0000_0000_0010L,
            Bit06 = 0x0000_0000_0000_0020L,
            Bit07 = 0x0000_0000_0000_0040L,
            Bit08 = 0x0000_0000_0000_0080L,
            Bit09 = 0x0000_0000_0000_0100L,
            Bit10 = 0x0000_0000_0000_0200L,
            Bit11 = 0x0000_0000_0000_0400L,
            Bit12 = 0x0000_0000_0000_0800L,
            Bit13 = 0x0000_0000_0000_1000L,
            Bit14 = 0x0000_0000_0000_2000L,
            Bit15 = 0x0000_0000_0000_4000L,
            Bit16 = 0x0000_0000_0000_8000L,
            Bit17 = 0x0000_0000_0001_0000L,
            Bit18 = 0x0000_0000_0002_0000L,
            Bit19 = 0x0000_0000_0004_0000L,
            Bit20 = 0x0000_0000_0008_0000L,
            Bit21 = 0x0000_0000_0010_0000L,
            Bit22 = 0x0000_0000_0020_0000L,
            Bit23 = 0x0000_0000_0040_0000L,
            Bit24 = 0x0000_0000_0080_0000L,
            Bit25 = 0x0000_0000_0100_0000L,
            Bit26 = 0x0000_0000_0200_0000L,
            Bit27 = 0x0000_0000_0400_0000L,
            Bit28 = 0x0000_0000_0800_0000L,
            Bit29 = 0x0000_0000_1000_0000L,
            Bit30 = 0x0000_0000_2000_0000L,
            Bit31 = 0x0000_0000_4000_0000L,
            Bit32 = 0x0000_0000_8000_0000L,
            Bit33 = 0x0000_0001_0000_0000L,
            Bit34 = 0x0000_0002_0000_0000L,
            Bit35 = 0x0000_0004_0000_0000L,
            Bit36 = 0x0000_0008_0000_0000L,
            Bit37 = 0x0000_0010_0000_0000L,
            Bit38 = 0x0000_0020_0000_0000L,
            Bit39 = 0x0000_0040_0000_0000L,
            Bit40 = 0x0000_0080_0000_0000L,
            Bit41 = 0x0000_0100_0000_0000L,
            Bit42 = 0x0000_0200_0000_0000L,
            Bit43 = 0x0000_0400_0000_0000L,
            Bit44 = 0x0000_0800_0000_0000L,
            Bit45 = 0x0000_1000_0000_0000L,
            Bit46 = 0x0000_2000_0000_0000L,
            Bit47 = 0x0000_4000_0000_0000L,
            Bit48 = 0x0000_8000_0000_0000L,
            Bit49 = 0x0001_0000_0000_0000L,
            Bit50 = 0x0002_0000_0000_0000L,
            Bit51 = 0x0004_0000_0000_0000L,
            Bit52 = 0x0008_0000_0000_0000L,
            Bit53 = 0x0010_0000_0000_0000L,
            Bit54 = 0x0020_0000_0000_0000L,
            Bit55 = 0x0040_0000_0000_0000L,
            Bit56 = 0x0080_0000_0000_0000L,
            Bit57 = 0x0100_0000_0000_0000L,
            Bit58 = 0x0200_0000_0000_0000L,
            Bit59 = 0x0400_0000_0000_0000L,
            Bit60 = 0x0800_0000_0000_0000L,
            Bit61 = 0x1000_0000_0000_0000L,
            Bit62 = 0x2000_0000_0000_0000L,
            Bit63 = 0x4000_0000_0000_0000L,
            Bit64 = 0x8000_0000_0000_0000L,
        }