Do you have a specific example? Typically if they're all present then yes you get all three. A Slam doesn't necessarily use your arms, it could be a body check or shoulder slam.
If the attacks are assigned to limbs then it's expected that you'll need to limit your attacks by those.
BTW, 2 limbs? Is this character a double amputee or something?
The soulknife feral heart claws use hands specifically, but the war hulk slam does not use anything in particular. It could be bashing your body into the target, it could be a kick, you could be using your head for once. I think you can use both.
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It is third-party material, so not exactly something under Paizo rules, but RAW I think you can use both.
RAI I am less convinced, as both abilities have a progression that is meant to keep useful. It all depends on what is an acceptable level of power in your campaign.
Note that you will lose a lot of damage from the slam attack by adding the claw attacks. The slam is a single attack and would normally get the effect of bonus a 2 handed weapon/single natural attack (-1/+3). But as soon as you add the ability to get claws it changes as one of multiple attacks and gets the -1/+2 benefits, even when used alone.