To check how many kills you have with each vehicle go to http://battlelog.battlefield.com/bf3/gate/
Sign in and then on the top right of the page there will be a stats symbol, click this then the vehicle tab and there you go.
For this you will have to get a kill with the following vehicles. The F35B fighter jet, the BTR-90 infantry fighting vehicle and the DPV fast transport vehicle (buggy).
Pictures of the vehicles can be found here.http://t3.gstatic.com/images?q=tbn:ANd9GcSOaPL0J5jU7g0RWkGWP...
Below are the maps that the vehicles are found on
F35B-Gulf of oman, Wake Island (US Side only)
Spawns at the US spawns on both maps, easiest if you just wait then spawn straight into the vehicle.
(If your having a hard time getting a kill with your jet an easy way to level up your jet so you can make getting the kill with it that one bit easier which has been pointed out by XPaTr0l on one of my other solutions is to play with a friend and choose the support class. Before you get in a jet, throw an ammo pack. Get in the jet, fly around when your friend is collecting your ammunition. The points you will get will count as point for the jet. You can get 100 points when your friend is reloading his gun. So you can unlock the missiles in one game.)
Most common on Wake Island and can be found at all of the flag locations.
BTR-90-Gulf of oman,Strike on Karkand, Sharqi peninsula
The easiest place to find it would be on the gulf of oman on conquest. It can be found at th RU spawn and at D when its under RU control.
These do not all have be done in one game.