If you pick the Mortal Weakness option, no. Both are fire weakness 10, you don't stack them up.
But if you pick up Antithesis it's another matter:
It goes back to the age old question about damage instances that's been left unanswered since pf2 came out.
To give a simple example, let's say that the creature was weak to slashing and weak to fire, and you hit with a flaming sword.
Half the community will say that the slashing and the fire damage are 2 instances so you apply both weaknesses (this is also the way the VTTs are handling it), the other half will say that it's 1 instance and they won't stack.
It's easier to answer when the damage comes from 1 source and is just modified by Traits, like a holy slashing attack, or the example given, cold iron+slashing, only does 1 instance of damage, so you would only apply the highest. Similarily, if as a Thaumaturge you do slashing+Antithesis, again, 1 instance, 1 weakness.
But in case of seperate damage sources, like runes that add a additional damage die and such, it's anyone's guess how that works.
Again, since there's no consensus how to properly run such scenarios, it's better to ask the GM how he's running it in his campaign.
