I believe 'mount', in this instance means something similar to 'amount'. So the sentence means that there was increasing evidence that Sempill was trading Britain's secrets to Japan. 'A flyer' is someone who flies aircrafts, although I've mostly seen it written as 'flier' :)

In the first example, "mount" means "build up". More and more evidence was found. I had to find the original text for the second example, and "flyer" means "pilot" in that context. It's not so clear because of the other sentences in between.