"My older brother does not like flying."

Translation: 我的哥哥不喜欢坐飞机。

[PeaceJoyPancakes]

As Duo is an owl, technically "不喜欢飞" should be acceptable. ;-)

[MaryAnnHeb]

I thought family members did not require a "de".

[kingstrider]

No, they normally don't, but it's not wrong to add one either. If you wrote the sentence without the 的 it should be accepted.