Mike,
You’ve got it – adding “style=” is the key.
Here’s the relevant section from the Documentation tab:
Support for “Photonic Gallery for Flickr, Picasa, SmugMug, 500px and Instagram”
The Photonic Gallery for Flickr, Picasa, SmugMug, 500px and Instagram plugin adds several new parameters to the [mla_gallery] shortcode to enhance your galleries. All you have to do is install the plugin, then add a “style=” parameter to your [mla_gallery] shortcode to use the Photonic styling and markup in place of the native [mla_gallery] style and markup templates.
You can use the “Photonic” screen of the Insert Media dialog to build the display portion of your shortcode parameters. After you click “Insert into post”, change the shortcode name from “gallery” to “mla_gallery” and add the query parameters you need to select the attachments for the gallery. The [mla_gallery] code will compile the list of attachments for your gallery, then hand control over to Photonic to format the results.