I am using Slick Slider within Magnific Popup.
The slider can contain a couple of items, and has it's own thumbnail nav.
Because the popup sets the slider to display:none I've use:
$('.slider-products').slick('setPosition');
within a callback function when the popup opens and changes.
I've created a pen.
You'll see a couple of issues, firstly the thumbnail navigation doesn't load in correctly due to the setPosition not being set, but I've been unable to get this to work. If you resize the window you'll see it.
Secondly on the second (purple) and third (green) items do not start on their first items. Each slider gets it's own unique class, so they shouldn't be interfering with each other.