It's not called doubled sex linked as there are multiple genes located on the Z sex chromosome. But the hen is both Sex linked Barred(or one of the multiple sex linked barring allelic mutations like Sex linked Dilution B^Sd or sex linked extreme Dilution) and Silver at the Z locus.
I just coined the term double sex linked since a single z chromosome is carrying two sex linked traits/genes, if a single z is carrying 3 sex linked genes then i'd call it triple sex linked or multiple sex linked if the case may be and just identify which sex linked mutations there are.
This naming convention helps me identify and differentiate for example a rooster that is ZB ZS vs another rooster that is ZBS Z+; both roosters will have similar phenotypes but their Z chromosomes are different. When the two roosters are bred they will produce different outcomes.
For example, when a ZB ZS roo is mated to ...using the punnett square, ZB and ZS will separate while in the double sex linked, ZBS Z+, based on the punnett square, the two Z chromosomes will separate as ZBS and Z+
So for me, calling a rooster double sex linked for barring and silver, means the pair of z sex chromosomes is ZBS Z+ . For the hen if she is silver barred at the same time then there is only one possiblity, ZBS double linked, since hens only have one Z chromosome.
This rooster below is double sex linked silver barred ZSB Z+ not ZS ZB.
Maybe this discussion regarding the the difference between a ZSB Z+ vs ZS ZB should be in a different thread. ZSB ZSB, ZS ZB, ZSB Z+, ZSB ZS, ZSB ZB.