I assume you are wanting to use American Airlines miles for this award.

The following would cost 130,000 miles for a business class and 180,000 miles for a first class award:
DFW-LHR-BKK-DFW (19,698 countable trip miles)

The following would cost 150,000 miles for a business class and 230,000 miles for a first class award:
DFW-SYD-HKG-BKK-LHR-DFW (24,896 countable trip miles)
DFW-SYD-SIN-HKG-LHR-DFW (24,817 countable trip miles)

The following would cost 190,000 miles for a business class and 280,000 miles for a first class award:
DFW-HKG-SYD-BKK-LHR-DFW (28,073 countable trip miles)
DFW-HKG-SYD-SIN-LHR-DFW (28,126 countable trip miles)

Obviously, the order you travel to these cities makes a big difference in the cost of the award.

The above assumes that you would have a stopover in each city (and in no other cities).

I recommend that you review this thread.