Translation:My little brother is writing a letter to a girl in the US in English.
Just because it is one sentence doesn't mean you can't pause somewhere, even if there aren't commas. If you do, the most natural place(s) to do so would be at one or more transition points between components of the constituent structure. Think subject, object, and prepositional phrases in English and components in Japanese ending with structural particles such as は, が, を, に, で, ... or non-final verb forms at the end of a clause (V-te, V-i: 書いて, 書き... though NOT as here in front of a helping verb, because that wouldn't be clause final), but not の when used simply to make a modifier of the preceding (pro)noun.
However, unless you really have trouble getting out more than a few words at a time or the person you're speaking to has trouble understanding, you will probably choose just one or two potential break points. Although it may be easier for language learners, speech that is too chopped up can be more difficult for fluent speakers to follow the total meaning of.
おとうとは / アメリカの女の子に / 英語で (/) てがみを書いています。
My younger brother / is writing a letter (/) in English / to an American girl.
It's not wrong, but whereas simple pronoun indirect objects are most frequently put in that position before the direct object, the more complex an indirect object is, the more likely it is to be placed after the direct object, preceded by 'to.' Otherwise, it may sound a little more awkward or difficult to understand. E.g.: I gave my sister-in-law who has been living in Boston (for ten years) a book.
That should be okay. I don't know if Duo is still rejecting it. Bear in mind, however, that your sentence contains three differences from the current default version (LITTLE brother, letterS, & American girl). I report many alternatives myself, and have had many accepted, usually quite some time afterwards. I know it frustrates us, but entering all possible combinations of all acceptable, alternative elements is a daunting task, that probably has practical limits.
I don't find that natural English at all, but I gather that "to write X" (vs "to write to X") is a common enough American usage. Either way it shouldn't be marked "wrong", they could just note that they expected a "to" in there. It's supposed to be a Japanese course, not an English one.