I have recently begun practicing escrima, and I find it difficult to simultaneously wield two sticks while keeping co-ordination and rhythm.
Are there some drills I could do on my own to improve my ability to use both hands at once?
I don't practice Escrima, so you will have to adapt.
Practicing both hands starts in your daily life. (See: http://martialarts.stackexchange.com/a/66/65) Generally, be aware of when you are comfortable doing something with one hand, and deliberately trying it with the other hand instead. Examples:
This will take a while. You do this while practicing your art. Over time, the movements in your art will show up in your day-to-day motions without conscious thought.
As for the art itself:
In the case of that figure-8 weaving pattern that seems common among dual-weapon techniques, I ended up spending six hours trying to get the rhythm. By this time, I'm already doing little things with either hand without thinking. In spite of that, that particular weave was still difficult ... probably as difficult as someone learning to play a piano piece where both hands play a different, phase-shifted melody line (like a Bach fugue).
I tried working off the video, but this did not go anywhere. Since I have skill at programming computers, I made up a notation system to describe the pattern. Then, I brute-forced it. I look at the notation and just moved my hands. (This might not work for you). Eventually, I'd have flashes where it gelled, like the weapons were weaving themselves. Then I became aware of it and it was gone. I would keep going until it gelled for a brief moment again. Eventually, I gave up, went to bed. when I woke up the next day, I was able to flow into the rhythm. The rest of the practice went into making things smoother, varying striking angle and blade facing, playing with footwork, etc.
From the bits of Escrima I've done, there's usually a set of drills - "Heaven 6" and "Earth 6", you can do them with a partner or do the forms by yourself. Doing those will get your comfortable with moving both hands at the same time.
Mostly the trick is that you have to learn the movements to maneuver the weapons around your arms without hitting yourself or locking up your own flow. Doing those over and over will give you some basic movements that work well.
Once you have those in mind, the rest of it becomes variations or sections of it and it becomes a lot easier to do new movements or variations.
Don't think of it as two sticks; think of it as one stick.
The human brain is not good at multitasking. You can only do one thing at a time, but you can do that one thing extremely well. As you get more comfortable with a simple task, you can make it more complex, and your brain learns to understand a more complex combination of movements as a single task.
I mostly agree with Ho-Sheng Hsiao's answer. The only real difference in how we do things is that we tend to practice offhand first, though we tend to do both in the same session back-to-back, but everything else fits with my experience on training coordination between the hands. I did want to add the following, since it is how I do this with two sticks:
Slow things down and work on getting everything right. Speed comes from repetition, so start by going slowly through whatever patterns you are doing. Work on getting the flow down and to keeping a consistent speed. Then, as you keep practicing, slowly increase that speed.
Then, past that, practice the motions daily. A bit like learning the piano: changing the overall speed of a piece while trying to keep the flow, focusing on basics and drills, and daily practice are a great way to get better quickly.