The molotov is ONLY available when playing as the Russians. To first unlock them, you must be any of the following: Level 9 Assault, Level 6 Support, Level 3 Automatic Rifleman, or Level 6 Rifleman.
Once you spawn in playing as the Soviet Union, just equip the molotovs using down on the D-Pad and the very first one you throw will unlock this achievement.
You will now have 99 remaining to throw for the 100 molotovs achievement. Remember that every life you will always spawn with 2. You can also refill your molotovs if a support member of your squad/team is playing the subclass that allows them to drop explosive ammo crates too.
Lastly, just bear in mind the Russians do NOT get the flamethrower, but you may still make progress toward all other non-flamethrower DLC achievements while playing as the Russians. Happy Hunting!