Can I control two coreless DC motors using L293DD SMD IC? I wish to control two 3.7V 6x12mm Coreless DC motors (both direction and speed individually). The only constraint is that the motor driver (circuit) has to be as small as possible. 

I've seen couple of driver circuits used in quadcopters where a single FET (such as IRLML2502) is used to control the speed of coreless motors. However, the direction control is not possible with such a circuit. 



It requires at least 6 MOSFETs and maybe Schottky diodes to prevent back EMF (similar to half H-bridge like here). Even after this, opposite direction control for two motors at once cannot be achieved. Then I figured all of this will increase the area required and decided to replace it with L293DD IC. Now my question is:


Can the L293DD SMD IC be used to control these motors? 
Is there an alternate solution/circuit/IC which can minimize the size and area? 
Are ESCs required for these small coreless motors? Can they be controlled directly via the L293DD (like normal motors)?


PS: The controller will be ESP8266 and the entire system will powered by a 3.7V 300mAh LiPo battery.
Can the L293DD SMD IC be used to control these motors?


Yes


  Is there an alternate solution/circuit/IC which can minimize the size and area?


Any of the more modern MOSFET based H-Bridge drivers that exhibit far less loss than the antiquated l293d


  Are ESCs required for these small coreless motors? 


No


  Can they be controlled directly via the L293DD (like normal motors)?


Yes

The L293 is old and, well, basically crap. For efficient battery based operation you realy need to be looking for something a little more modern and efficient. There's length to choose from - take a look on your favourite electronics supplier (which means not Amazon...)