Because the second "had" is about owning more money and the first "had" is to make a past tense. They would fly to Canberra if they had more money. - Present tense. They would have flown to Canberra if they had had more money. - Past tense. Hopefully a linguist or teacher will be able to give a more technical answer, but that is why.

They would have flown to Canberra if they had more money. The example is a mix of type 2 and 3. Here are correct type 1, 2, and 3 variations. Type 1 - Real present/future situation If they have enough money, they will fly to Canberra. They will fly to Canberra if they have enough money. [The speaker believes that it is plausible that they will have enough money.] Type 2 - Unreal present/future situation. If they had enough money, they would fly to Canberra. They would fly to Canberra if they had enough money. [The speaker believes that it is implausible that they will have enough money. Here "if they had" is in a past form to indicate an unreal present or future situation. An alternate is "if they were to have" to indicate an unreal present or future situation.] Type 3 - Unreal past situation. If they had had enough money, they would have flown to Canberra. They would have flown to Canberra if they had had enough money. More information here: https://www.ef.com/ca/english-resources/english-grammar/conditional/

This may sound ridiculous...The second "had" is about money in their wallet. The first "had" is a part of my description of an event that happened last week. Sorry so silly!

They would have flown to Canberra if they had had more money.

type 3: If (Past Perfect), (Future in the Past Perfect): If they had had more money, they would have flown to Canberra. (Past Perfect means: had +past participle)