You can enable drag & drop of images while submitting the forms.
Note: Each image will create a new post with same title, category, tags you have entered. As like other plugins it will not create group of galleries. This is the place where most of the users get confused.
Later with the help of [flexi-gallery] shortcode, you can make galleries of your choice.

[flexi-form class="xxx_class" title="Submit to Flexi" name="my_form" ajax="true"]
  [flexi-form-tag type="post_title" title="Title" value="" placeholder="main title"]
  [flexi-form-tag type="category" title="Select category" ]
  [flexi-form-tag type="tag" title="Insert tag"]
  [flexi-form-tag type="file_multiple" title="Drag & Drop multiple files" class="flexi_drag_file" multiple="true"]
  [flexi-form-tag type="submit" name="submit" value="Submit Now"]
[/flexi-form]

Copy/paste above code to any of your page. Link it as submission page if necessary or it can work independently.