What kind of impact would it have on my karma if I kill an insect, or a fly? Is that a sin?

The dharma prescribed varies as per the Ashrama. that is, if one is a Sanyasi – (a renounced person), the prescribed norms are very stringent. If he kills an insect even if it harms him it is a sin. He is not allowed to do so. but for a householder, it is different. If an insect harms him, he can kill it, if necessary. That would not amount to a sin. but if he does it purposefully or for pleasure it is a sin.
Shastras state that if a person kills helpless beings like insects and flies, he will contract skin diseases in his future birth.
In short, a householder can kill an insect as an act of self-defense if harmed by it. It is not a sin.