I play with the Insect Glaive quite a bit and I'm stuck with the default Kinsects. Any idea as to how to get new Kinsects?
You can purchase, upgrade, and change the element of Kinsects the same way you would craft and upgrade weapons, at the smithy.
Kinsects have two trees, or "lineages", starting from either the Mauldrone, which deals blunt damage, or the Culldrone, which deals cutting damage. These trees are revealed as you obtain the required items, just like weapon trees.
Each base kinsect has an upgrade tree similar to other weapons. As you upgrade it you will eventually have to choose a branch to continue on, and many of these drastically change the look and damage your kinsect does.