RDM has nothing to do with Slashing. Its enchanted melee combo is magic, non-enchanted along with the oGCDs are Physical Pierce.
Even if SAM and NIN are present there are a few interesting facts (and benefits) about this slashing debuff:
1- WAR accesses it on second GCD whereas SAM applies it for the first time a bit late depending on which opener they use. i.e. on about the 9th GCD in 1 Sen Hagakure openers. NIN applies on 3rd GCD regardless. It does not matter THAT much since it's only at the beginning of each fight or after boss invulnerability periods.
2- The order is: SAM, WAR, NIN SAM's debuff overwrites WAR's but is longer. NIN's debuff is overwritten by WAR's because it's shorter. I believe 30 > 24 > 21 for SAM, WAR and NIN respectively.
3- This really follows the above points but deserves to be its own since it is a bit detailed:
In the natural DPS rotation, WAR applies Maim every combo from their second hit. Even if you need to build enmity, Butcher's Block doesn't need to be used more than once every Storm's Eye duration. This benefits the slashing DPS jobs in an interesting way.
SAM wants to cycle different combos for Sen. When SAM wants to apply Higanbana (the DoT) it needs 1 Sen. If you know the other person will reapply it before it falls off, SAM can rearrange its combos for a choice of extending a buff early or using the faster Sen from the 2 step combo Yukikaze.
With either of the other two present, NIN can allow its slashing debuff to fall off for just under 2 seconds to allow a full Shadow Fang DoT instead of clipping it early to ensure slashing debuff doesn't fall off. This may also add another Aeolian Edge combo.
DISCLAIMER: Take this with a grain of salt as I do not main SAM nor NIN but I play them on and off on an alt character. The info above is what I picked up from other NIN/SAM players and may not necessarily be adequate DPS gains. If so I stand corrected and would not mind being told the correct way.