Module with helper functions to initialize or reinitialize a Slick carousel
This approach seems fine. I did notice the following loop in Helpers. executeFunctionByName():


for (var i = 0; i &lt; namespaces.length; i++) {
  context = context[namespaces[i]];
}
return context[func].apply(context, args);



Doesn't that just set context equal to the last element in namespaces? Why not just use a simple assignment without a loop?



The value for the timeout


 var timeout = 340;



Could be declared with all capitals as is idiomatic in JavaScript and many C-based languages, as well as a more descriptive name:

 const RESIZE_TIMEOUT = 340;




There are a few things that could be simplified.

In Carousel.init the resize callback could be simplified from


$(window).on('resize', Helpers.debounce(function() {
  applyForTheseQueries();
}, timeout));



To this:

$(window).on('resize', Helpers.debounce(applyForTheseQueries, timeout));


And if ecmascript-6 syntax is supported, then object initializer shorthand notation can be used - instead of :


return {
  init: init
}



just use:

return {
  init
}


And instead of 


return {
  executeFunctionByName: executeFunctionByName,
  debounce: debounce
};



Simply to 

return {
  executeFunctionByName,
  debounce
};


Another ecmascript-6 feature that could be used is the for...of loop. Instead of 


for (var i = 0; i &lt; namespaces.length; i++) {
  context = context[namespaces[i]];
}



Simplify this to 

for (const namespace of namespaces) {
  context = context[namespace];
}