Hooty and Duo have not met in canon as Hooty is part of the Disney animated series The Owl House, and Duo is the mascot for the language-learning platform Duolingo.
While not technically canon the series creator of The Owl House, Dana Terrace, tweeted that "Friends, Hooty and the Duolingo owl are BITTER rivals in the bird industry. Please respect their wishes and do not, I repeat, DO NOT draw them as friends in any way shape or form.", before adding "I have just been informed that Hooty and the Dualingo owl have reluctantly teamed up against a mutual enemy: The Owls of Ga'Hoole. After the bloody battle they apparently developed a begrudging respect for each other. Proceed with that in mind." During a reddit AMA, Dana Terrace joked she was pitching an Owl House spin-off series about Hooty and Duolingo's romance.
Aside from the backstory given by Terrace, Hooty and Duo have other shared qualities; the obvious that they are both owl mascots for their respective platforms. They also both encourage learning, as Hooty brings Luz her books and sees her off to school and Duo helps users learn additional languages. They both have links with Spanish language as Duolingo's first language course was for Spanish and Luz Noceda, the most recent addition to the owl house that Hooty protects, is a Dominican-American who is also fluent in both Spanish and English.
Dana Terrace further confirmed Hooty and Duo's friendship when the official Duolingo Twitter account posted art of Duo and Hooty watching the first episode of The Owl House's second season. Dana Terrace stated that, "Hooty and Duo only watch cartoons after they finish their Spanish lessons./Once enemies, now mentor and mentee. Their bitter rivalry was set aside when Hooty decided he wanted to impress Luz’s mom if they ever met. This is CANON." 
Following Terrace's tweet fans quickly drew the pair hanging out, being friends. Duolingo's official twitter responded the next day and an illustrator for Duolingo drew them together in the official style, causing more to become aware of their crossover friendship. Many reacted with horror and delight over the creation of such a crackship. While a lot of people ship Hootlingo as a friendship, the majority of Hootlingo shippers ship it as slash ship. There are currently 28+ works on AO3 depicting the pairing romantically.
|SHIPS||het||Huntlow • Lunter • Sking|
|slash||Goldric • Guster • Gustholomule|
|femslash||Amillow • Boschlow • Lumity • Luzanne • Willuz|
|friendships||Aminter • Hoolith • Hootlingo • Ledaking • Luzking • Owluz|
|poly||Luzblights • Willumity|
|family||Belonter • Blight Siblings • Blight Twins • Clawthorne Sisters • Dadrius • Edaking • Luzeda • Owl House Family|
|CHARACTERS||female||Amity Blight • Eda Clawthorne • Luz Noceda • Willow Park|
|male||Edric Blight • King Clawthorne|