During this Hawai'ian-to-English exercise, the "special characters" are not shown below the input text box, but we are apparently still expected to type the Hawai'ian names with macrons and glottal stop signs. Duo should either let names in the English reply be entered with a different convention, or enable the spacial character entry buttons.
On my MacBook Pro (an Apple computer) I added the Hawaiian key board so I could easily type the Hawaiian characters. Click the U.S. icon at the top right of your computer screen or click the search at the top right of your screen and type in keyboard. The keyboard preferences open. Click Input Sources, then Click the + key to add a new keyboard. Look for Hawaiian.
As mentioned before, you can use the apostrophe as the 'okina.
As far as the kahakō, apple users should be fine on their phones. All one would need to do, I believe but it has been years since I have used an iPhone, is to hold the letter and other options appear including the vowel with a kahakō.
Android users are a bit trickier, but a kahakō can be used for all vowels except an o. All you need to do to access it is to hold on to the vowel until your additional options appear and then press the vowel with the kahakō. As for the "o", it does not have this option. HOWEVER, it does not mark you wrong if you use a regualr "o" with no markings. FYI... This is how we, in Hawai'i, text others in 'ōlelo Hawai'i...