I'd suggest letting him play at his own pace (unless he's an experienced MMORPG player starting WoW for a specific end-game purpose such as raiding / PVP). In particular if he's new to the genre, that first time exploring the world is such an amazing time, it would be a shame to be boosted through it.
Following the 'Shattering' the starter zones have had an overhaul and are fun to play through and also give a better step by step introduction to game mechanics and how to play your class.
Also the levelling speed now is pretty crazy - people in my guild are making jokes about being level 30 by lunchtime! It's not quite that fast, but if he gets into it he'll be 30 before he knows it.
Using a flight point is equivalent to a 333% speed mount, slightly faster than even Master Riding. But that speed is negated by the use of the scenic routes you mentioned.
So, if you have Master Riding and you can take a direct, as-the-crow-flies path, it'll almost always be faster to do it yourself. If you only have Artisan Flying, it'll only be faster if the flight path is really roundabout. If you only have Expert Riding, you might as well use your ground mount, as even it's faster.
It's a good thing to note that there are still mount speed increasing effects in the game, which can affect the choice between doing it yourself and taking the flight path:
None of these effects stack with anything else (i.e. you can't combine Crusader Aura with any of the others, even Pursuit of Justice), but they are multiplicative. So, if you have Crusader Aura and Master Riding, you wind up with the equivalent of a 392% speed mount; 17% faster than the flight path.
And to clarify, the formula for calculating movement speed is:
(100 + Mount Speed) * (1 + Mount Speed Effect / 100) - 100
So, with Crusader Aura and Master Riding:
(100 + 310) * (1 + 20 / 100) - 100
410 * 1.2 - 100
392%
Best Answer
Yes, using battle stones to level your pets counts towards the Pro Pet Group achievement which you need to unlock the Celestial Tournament.
I have leveled several pets with battle stones and have confirmed they counted towards the achievement.