We have a teak handmade kayak frame and we are trying to figure out how much it is worth so that we can sell it.

I'm not sure what online auction options you have. Here in NZ, I'd wait until Spring and then list it for a starting price of $1 and let the market decide. I'm not sure it would be worth more than the materials.

The unfortunate reality is that you are selling something 20 years old and unfinished. So whoever buys it has to first satisfy themselves that it is fit for purpose, then gain familiarity with the build in order to finish it.