A working example of nested forms just using Reform.

_form.html.erb

#views/users/_form.html.erb
<%= simple_form_for @form do |f| %>
  <%= f.error_notification %>
	
  <%= f.input :name %>
  <%= f.input :email %>


  <h4>
    <%= link_to_add_fields icon(:plus), 
         f, 
         :assignments, 
         class: "btn btn-success", 
         append_selector: "#user_assignments tbody tr:first",
         new_object: AssignmentForm.new(Assignment.new) %> 
        Assignments
  </h4>
  <table class="table table-hover table-bordered" id="user_assignments">
    <thead>
      <tr>
  	<th>Assignment</th>
  	<th></th>
      </tr>
    </thead>
    <tbody>
      <%= f.simple_fields_for :assignments do |builder| %>
        <tr>
	  <td>
	    <%= f.input :assignment_id, 
	                label: false,
		        collection: @assignments,
			prompt: "Select a assignment" %>
	  </td>

	  <td>
	    <%= f.hidden_field :_destroy, class: "destroy-input" %><!--Set via javascript on click of remove button -->
	    <%= link_to "Remove", '#', class: "remove_fields btn btn-xs btn-danger" %></td>
	  </td>
        </tr>
      <% end %>
    </tbody>
  </table>

  <%= f.button :submit %> <%= link_to "Cancel", :back, class: 'btn btn-warning' %>
<% end %>

assignment.rb

#models/assignment.rb
class Assignment < ActiveRecord::Base
  belongs_to :user
end #class Assignment

assignment_form.rb

#forms/assignment_form.rb
class AssignmentForm < Reform::Form
  property :id, type: Integer, writeable: false
  property :_destroy, virtual: true
  property :assignment_id, type: Integer

  validation :default do
    key(:assignments_id) { |assignment_id| assignment_id.filled? & assignment_id.int?  }
  end
end #class AssignmentForm

nested_form.rb

#forms/reform/nested_form.rb
module Reform
  module NestedForm
    extend ActiveSupport::Concern #might not be needed... Infact probably isn't
    def nested_removeable!(collection:, fragment:, binding:, **)
      deserialized_item = collection.find { |item| item.id.to_s == fragment["id"] } if fragment["id"].present?
      
      if fragment["_destroy"] == "true" # don't process if it's getting removed!
        collection.delete(deserialized_item) if deserialized_item.present?        
        return skip!
      else
        return deserialized_item || collection.append(model.send(binding.name).new)
      end
    end
  end
end

nested_forms.js.coffee

#assets/javascripts/nested_forms.js.coffee

#add fields to form. used by nested forms
$.fn.addFields = (id, fields) ->
  time = new Date().getTime()
  id = new RegExp(id, "g")
  fields = $(fields.replace(id, time))
  this.before(fields)

#remove fields from form. used by nested forms
$.fn.removeFields = (destroyInputSelector = ".destroy-input") ->
  this.find(destroyInputSelector).val('true')
  this.hide()
  this

jQuery ->
#enables add and remove fields from nested forms
  $('form').on 'click', '.remove_fields', (event) ->
    $($(this).attr("data-fields-selector")).removeFields()
    event.preventDefault()

  $('form').on 'click', '.add_fields', (event) ->
    $($(this).data("append-selector")).addFields($(this).data('id'), $(this).data('fields'))
    event.preventDefault()
    

user.rb

#models/user.rb
class User < ActiveRecord::Base
  has_many :assignments
end #class User

user_form.rb

#forms/user_form.rb
class UserForm < Reform::Form
  include Reform::NestedForm
  
  property :name
  property :email

  collection :assignments, populator: :nested_removeable!, skip_if: :all_blank, form: AssignmentForm

  def prepopulate!(options={})
    return if model.client.blank?
    self.assignments << model.assignments.new if assignments.size == 0
  end

end #class UserForm

You are using a link_to_add_fields helper method in your view but this is not defined anywhere in this gist. Where does this come from?