hi there,i dont think you will be entitled to a new floor to be honest but thats just my opinion,it seems from what you have said that you employed a kitchen fitter and not a tiler to carry out the worknot saying a kitchen fitter doesnt know how to tile as some of them do but its not really his main trade is it.
also if you supplied 6mm ply and this guy didnt even want to lay it that should have sent alarm bells going,tiles havent cracked or grout cracked just a slight creak in one area ...that doesnt warrant a new floor...the guy might just turn round and say there was no creak when he laid it? you cant argue against that
i do agree though the only way to resolve this creak is to remove the offending tiles....however if you have spares and the current 6mm ply install hasnt failed you could lift the offending area and remove the ply and also chipboard,,,add strengthening and re sheet and re tile and use a 6mm cement sheet instead it might just solve the issue do you have any spares or can you get spares? let us know cheers