Duplicate reads have first been removed using picard:

java -jar -Xmx3g picard/dist/picard.jar MarkDuplicates INPUT=input.bam OUTPUT=output.bam METRICS_FILE=output.dup_metrics CREATE_INDEX=TRUE VALIDATION_STRINGENCY=SILENT

When I run samtools flagstat on the output bamfile I get the following:

2182812 + 0 in total (QC-passed reads + QC-failed reads)
226710 + 0 duplicates
2176925 + 0 mapped (99.73%:-nan%)
2182812 + 0 paired in sequencing
1091406 + 0 read1
1091406 + 0 read2
2156992 + 0 properly paired (98.82%:-nan%)
2171322 + 0 with itself and mate mapped
5603 + 0 singletons (0.26%:-nan%)
9776 + 0 with mate mapped to a different chr
7030 + 0 with mate mapped to a different chr (mapQ>=5)

So presumably the file still contains 226710 duplicate reads. If I filter out duplicates according to this table:

Flag        Chr     Description
0x0001      p       the read is paired in sequencing
0x0002      P       the read is mapped in a proper pair
0x0004      u       the query sequence itself is unmapped
0x0008      U       the mate is unmapped
0x0010      r       strand of the query (1 for reverse)
0x0020      R       strand of the mate
0x0040      1       the read is the first read in a pair
0x0080      2       the read is the second read in a pair
0x0100      s       the alignment is not primary
0x0200      f       the read fails platform/vendor quality checks
0x0400      d       the read is either a PCR or an optical duplicate

using the command:

samtools view -F 400 output.bam | wc -l

I get 506072, not: total reads (2182812) - duplicates (226710) = 1956102

My question is why does samtools flagstat indicate that there are still duplicates present after running picard tools, and why are these figures inconsistent when I attempt to filter out duplicates using samtools? I've been asked to remove duplicates for a project. At the moment I am very confused as to which method I should use given the inconsistencies in results.