What are the ways to burn fuel faster in case of emergency without fuel dumping system?
This question (sorry to say) is sort of moot because:


if you have an urgency to land (e.g. cargo fire), you don't care if you are overweight and you'd land anyway
if you have time to dump fuel, the situation isn't as desperate, and you can easily wait just a bit longer.


The large jets (e.g. Airbus A380, Boeing 777) have a fuel dumping system because, with full fuel, these planes can travel up to 12 hours or more! That is to say, if you don't dump fuel, you might have to fly around all day to get down to your normal landing weight.

Airbus A320 and Boeing 737 are different: they usually fly 1~3 hours route, and may stretch to 6 hours on a full tank. So, to begin with, you need less time to burn fuel. Plus, these (relatively) small planes can land on shorter runways, which means your airport choice will not be as restricted as with a large jet.



Now, as to actually answering your question......

Flaps and gears have speed restrictions. You cannot fly full throttle with these deployed. That being said, if the pilots put the airplane in landing configuration (full flaps + gear down), drag will increase significantly and they will need more thrust to maintain altitude and airspeed.

You can technically achieve that with spoilers, but it's dangerous. Spoilers destroy lift, so what you're really doing is reducing the effectiveness of your wings and compensate that by flying faster and/or increasing your angle of attack.

Then again, if you're desperate, just land right away......