How are the soldiers could stand and be on his back without Temeraire slashing out or blowing flames? He must be very docile.

Well.. probably you've not read the books x3 (they're great). In this world (the our own, with historical characters and so on.. + dragons), dragons lives with humans, they talk and are intelligent being (even if many are a bit dumb). Except for few wild dragons, in Europe almost all work in human western society in military: they're feared by normal people or politics in Europe only because they are thought to be fierce creatures, but they're not and they're very important for war. (in China, Africa or South America dragons are considered sometimes equal to humans and sometimes even more important).

And speaking about Temeraire, in this books only few dragons have fire, and while the Captain has a link with the dragon (being the human first being to welcome the dragon at the hatch) also a dragon think at the other soldiers of the crew as "his" men, they can be very possessive and can be mad if someone kill one of their humans.