Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
There is no impediment to working in a company that produces insect-killing chemicals, provided there is no other violation of Islamic rulings. Insects and animals that can harm are lawful to be killed. The Prophet (Sallallahu Alaihi wa Sallam) said: "Five kinds of animals are harmful and could be killed in the Haram (Sanctuary). These are: the crow, the kite, the scorpion, the mouse and the rabid dog." [Al-Bukhari]
Killing them is made lawful since they cause harm to human beings. The Prophet (Sallallahu Alaihi wa Sallam) also said: “If a house fly falls in the drink of anyone, he should dip it (in the drink), for one of its wings has a disease and the other has the cure for the disease”. [Al-Bukhari]
The above Ahadith proves the lawfulness of killing the above animals.
Allah knows best.