Conditional image style in Views
Add the image field twice(!) to the fields list. Use the frame style on the first image and the no-frame style on the second. Exclude both fields from display and place them before the checkbox.

Next, rewrite the output of the checkbox field to use [field_image] if the checkbox is checked (normal rewrite) and [field_image_1] if it is not (no result behaviour, Treat 0 as empty).