Is the assassin poison considered an alchemical item? As I read alchemist(Eberron) it states poison as an alchemical item.
Can someone with the alchemist feat make assassin poisons?
No they cannot.
Only Executioner Assassins with the Poison Use class feature can create assassin poisons. They function as the class's daily power use, and therefore are equivalent in power. Allowing them to be created by a character with the alchemy feat provides entirely too much utility to anyone with alchemy.