You can’t put forms directly into emails, this is a limitation of email itself, not of Infusionsoft.
A common alternative is to use a multiple-choice question as a trigger for the form and you make two or three buttons in your email for them to answer the question and then be directed to the form based on their choice of button. For example for a feedback response form, you can have two buttons in the email for “I’m a happy customer” or “I’m not happy with my service” and then load different feedback forms depending on which button they click.
You can use the URL for the campaign form as a link in your emails - someone else may have a more specific answer on the best way to do that.