Animate outputs an HTML file. Just create a form and copy and paste your form doc into your animate HTML doc and use CSS for positioning.
EmailMeForm has a free version. It is super easy to use.
Please ignore that. Animate recently added native support for jQuery components to Canvas documents. Just open the Components window (Ctrl+F7) and drag a TextInput component onto the stage.
Note that all Canvas mode components are just browser-native DOM elements that float above the stage canvas element, so nothing on the stage can appear above or mask them.