Either sentence could be correct with one minor change. "please help arrange packing for the order" the "the" before packing isn't necessary. Your first sentence is asking someone to get the materials to pack the order together. The second sentence is asking for the job of actually packing the order with the packaging materials to be arranged. Depending on your intent, either sentence could be correct. Hope that helps!

You can also say "Please help arrange the packaging of the order" , meaning to arrange to have it packaged.