All the SAM flags are stored in a bit field with each flag represented by a single bit. Bits set to 1 are on and bits set to 0 are off.

Using samtools flags with give you a list of all the flags.

0x1       1  PAIRED         paired-end / multiple-segment sequencing technology
0x2       2  PROPER_PAIR    each segment properly aligned according to aligner
0x4       4  UNMAP          segment unmapped
0x8       8  MUNMAP         next segment in the template unmapped
0x10     16  REVERSE        SEQ is reverse complemented
0x20     32  MREVERSE       SEQ of next segment in template is rev.complemented
0x40     64  READ1          the first segment in the template
0x80    128  READ2          the last segment in the template
0x100   256  SECONDARY      secondary alignment
0x200   512  QCFAIL         not passing quality controls or other filters
0x400  1024  DUP            PCR or optical duplicate
0x800  2048  SUPPLEMENTARY  supplementary alignmentent

There is no primary flag. All reads are presumed to be primary unless another flag indicates that it is not. The flags that make a read not primary are (from the documentation) either 0x100 (SECONDARY) or 0x800 (SUPPLEMENTARY). Also, all reads are presumed to be mapped unless they are marked with the UNMAP flag.

We should make the documentation on flagstats clearer.

You can use samtools flags to tell you what a flag value means. So samtools flags 0x800 gives

0x800   2048    SUPPLEMENTARY

For multiple flags, add them together samtools flags 0x904 (0x4 + 0x100 + 0x800) gives

0x904   2308    UNMAP,SECONDARY,SUPPLEMENTARY

You can do the reverse samtools flags UNMAP,SECONDARY,SUPPLEMENTARY which also gives

0x904   2308    UNMAP,SECONDARY,SUPPLEMENTARY