Can I code the iframe code into an html button on my webpage?

I dont want to use just the iframe code as it needs to be contained within a button on my site and not just on it.

But I liked the feedback style button pinned to the left side of my site nut was causing complications.

I'm not sure if I understood how you would like to embed your form, may you please kindly take a look on the following guides: 

https://www.jotform.com/help/93-Creating-a-Feedback-Button

https://www.jotform.com/help/220-How-to-Create-a-Lightbox-Form

Note that the form will be always loaded within an iFrame, the different is that it shows only when the button is clicked. 

If you have questions, let us know.