The adjective rädd = afraid, scared, and is inflected as follows:
common: rädd
neuter: rätt
plural: rädda
However, according to Språkrådet, the neuter form, rätt, is rarely used.
Rädd is used in the following constructions:
rädd för = scared of something
rädd att +infinitive = scared of doing something
rädd för att +infinitive = scared to do something:
rädd för kärleken
afraid of love
rädd att flyga
fear of flying
rädd för att misslyckas
scared to fail
The inflections of rädd are also words in themselves. Rätt means both right (the adjective correct, and the noun, a legal right), and a dish or course at a meal.
The Swedish charity Rädda Barnen has nothing to do with scared children, but is Save the Children, where rädda = save, rescue, and räddare = rescuer.
One last word for you: nöd = need, distress; so:
en hjälpare i nöden
a friend in need
So, how do you translate the following?
Räddaren i nöden
Would you believe:
words from sweden 
How do you say “afraid of” and then a noun? Like “afraid of you”.
Interesting how I knew all the ways “rätt” is used, but didn’t realize it was the same word. As you use the language you just know the difference depending on the contex
Your example “rädd att flyga – fear of flying” made me pause. I would translate “fear of flying” with “flygrädsla” (rädsla/rädd is the noun/verb pair). This is also related to Hilary’s comment since “afraid of you/flying” is “rädd för dig/att flyga”.
Never having read “The Catcher in the Rye” I had to read the synopsis (on Wikipedia) before I understood the logic behind the translated title. I would guess that many people with a Swedish upbringing have never read this book.