I'll need to put some better documentation together, but most of this applies: http://www.formulate.rocks/articles/custom-field-types

The backend portions are identical, including the back office AngularJS.

You'll want to ignore the frontend AngularJS though. Instead, you'll use plain JavaScript. Here's a basic shell of what you'd need to do:

// Dependencies.
let ValidationUtil = require("/App_Plugins/formulate/templates/responsive.plain-javascript/utils/validation");

// Ensure fields have been initialized.
let key = "formulate-plain-js-fields";
window[key] = window[key] || [];

/**
 * Renders the field.
 * @param fieldData The field data that should be used to render the field.
 * @param fieldValidators The associative array of the field validating functions.
 * @param cssClasses The CSS classes to attach to the element.
 * @param extraOptions Additional options that are less commonly used.
 * @constructor
 */
function RenderAutoComplete(fieldData, fieldValidators, cssClasses, extraOptions) {
    //TODO: ...
}


/**
 * Returns the DOM element for the field.
 * @returns {Element} The DOM element.
 */
RenderAutoComplete.prototype.getElement = function () {
    return this.element;
};

/**
 * Adds the data for this field on the specified FormData instance.
 * @param data {FormData | any} The FormData instance or associative array.
 * @param options {{rawDataByAlias: boolean}} Optional. The options for setting the data.
 */
RenderAutoComplete.prototype.setData = function (data, options) {
    //TODO: ...
};

/**
 * Checks the validity of the value in this field (adding inline validation messages if necessary).
 * @returns {Promise[]} An array of promises that resolve to validation results.
 */
RenderAutoComplete.prototype.checkValidity = function () {
    //TODO: ...
};

// Add this field type to the window object so Formulate will pick it up.
window[key].push({
    key: "AutoCompleteField",
    renderer: RenderAutoComplete
});

Depends on if you have a JavaScript build step. If not, you'll need to extract some of the utility functions. You can find the ones for validation here: https://github.com/rhythmagency/formulate/blob/4d264e92d0ee8f20506c20f117498ea2853aaa74/src/formulate.frontend/responsive.plain-javascript/utils/validation.js