I am a little biased, but our DVD, Introduction to Aerial Archery will get you off to the best start possible and really shorten your learning curve. The link to our website in in my signature.
A couple things will really help. Practice getting to full draw, anchoring, and releasing as quickly as possible on stationary targets. Flushing birds are very agile after gaining stable flight and can actually dodge your arrows. So getting your arrow off while the birds are more vulnerable is important. Also, the faster the bird gets moving and the further the distance, the lead becomes significantly more challenging.
There are a lot of drills to do in between, but the final practice should be on actual clay pigeons out of a thrower. This will strongly reinforce the need to shoot fast and is the best practice you'll find for shooting at flushing birds.
With a lighter bow, you need to use the least amount of fletching possible while keeping your arrows safe and recoverable. You'll see on clay pigeons, that your arrows will not impact the clays with the same authority as it would on a stationary target. You may hit a clay pigeon and not even break it. Penetration suffers significantly on birds that are flying away. Your field tips with claws will likely leave you with disappointing results. With your setup, the main variables that will determine the lethality of your hits are the range of the bird, angle to the bird, and your fletching selection. If it's allowed and the dogs can be tethered, use broadheads. If not, try to avoid straight away shots even though they are the easiest. You will hit the birds so much harder if they flush towards you or present a crossing/quartering shot.
Last tip is safely shoot at everything that flies. Even hail mary shots have a chance. An arrow sitting on the bow will never kill anything.
Have fun!