Short answer - possibly.
Batteries have a wide range of capacities, typically measured in Amp-Hours (sometimes Watt-Hours) which is more-or-less how many hours the battery can supply 1 amp. The battery in my truck is 70Ah, so it could supply 28 amps for around 2.5 hours. Of course, this is a very rough estimate - the battery manufacturer will specify the allowable discharge rates and times. It's possible that my calculation is nowhere near accurate for that particular battery. You would have to check the rating of your batteries, which should specify the capacity and continuous amperage capability.
Two car batteries can safely be put in series to get a total voltage of 24 if
- they have the same ratings
- they are both charged
To ensure this, you should use two brand-new, identical batteries in series. Remember, series would be negative of battery 1 connected to positive of battery 2, with the total voltage across positive of battery 1 and negative of battery 2. Better yet, you could buy a single 24 V automotive battery (yes, these exist for special purpose vehicles).
First, and foremost, let me state that automotive batteries are designed with the specific purpose of delivering an instantaneous current of hundreds (sometimes thousands) of amps in order to start a car. That kind of power can kill you.
There might be better options
More commonly, car batteries are rated in CCA (Cold-cranking amps) which just means how many amps then can deliver at a freezing temperature for about 30 seconds without dropping the voltage too much. Car batteries are designed to put out a LOT of current all at once, then recharge while your car is running, not discharge slowly down to nothing then be recharged like other common batteries.
Lead acid batteries are really tough and versatile, and they will work for this purpose if they are rated for the power you need. A better option might be lithium batteries, many of which are designed to deliver a high continuous current load.
You also have to remember that car batteries see a high voltage drop under load. They are typically charged up to around 14V and can drop as low as 7.2 during extreme current usage. Without a voltage vs current chart, you would have to measure the voltage across your batteries during the expected current draw to know what to expect. The voltage will also drop over time as the charge depletes. Ensure your motors can handle this potential range of source voltage.
Double Check your Ratings
Power = Current * Voltage: 14A * 24V = 336 W. You stated their rating at 250W.
The current a motor draws and the voltage across its coils is also dependent upon the motor load. There are many types of DC motors that behave a bit differently. You'll need to provide more information about your motor and the batteries you have in mind to get a more precise answer.