My father sold shoes for most of his life. He was actually apprenticed to a shoe shop at the age of 14. so what follows is the voice of my father giving the benefit of 40 years in the trade (I suffered it, now it is your turn)
A good application of polish with a cloth to ALL leather surfaces, leave to "soak in" over night and buff up in the morning and your problem may go away. Remember to polish all the bits that one doesn't normally see ~under the laces, the surface of the tongue etc. I still polish the arch under all of my shoes .... such was his training and I am driven mad by people who walk around with the price label still stuck beneath their shoes.
Now shoes and boots come with a support built into the arch of the shoe. This runs from heel to sole and is often, in cheap shoes, of inferior quality metal. If the squeaking is coming from there it is because the support is loose and you will not be able to cure it without deconstructing the shoe/boot. Best throw them away and start again. You can tell if that is the cause of the squeaking because you will be able to feel it through your foot. You could try returning them as a complaint but most shoe shop assistants nowadays will not know how they are made and will look at you as if you are mad.
Lastly, an old saying whenever anyones footware was heard to be squeaking was "Time you paid for those boots and the bloody squeak will go away"
Ooooooooooooo .... It's an education this site ~ innit?
