The best way I know to get feedback to the developers is via the in-app feedback.
As for how to express your request... The following three lines are to illustrate the remainder of my answer:
The download option (using XML) from the Notes tool on LDS.org _is_ an export. (I'm a database application developer, so I'm using that term the way a computer person uses that term.)
Options 1 & 3 are not exports, but serve the purpose of recording your data in an alternate format for archival and emergency access (e.g. to re-key into another app).
Option 4 is better than an export, it's a copy of the database which you can use to your heart's content. Make regular backups, and you're gold. All you need is a SQLite DB editor (many free).
So, since none of that is what you want, my recommendations are: remove the word "print" - my #1 above is exactly what you said you wanted ("print a chapter of scripture complete with annotations"), but apparently you would prefer something else, so don't mention it. Leave out "archiving" (multiple of my replies will allow you to archive, but that's apparently not sufficient, so don't even mention it). Stick with the term "export", but you'll need to define what that means to you, because developers are going to think what I thought (there's already a way to export and one way to back up which is as good as export).
I recommend using another app which already does this as an example. Given your reply, I'm guessing you want an in-app feature (as opposed to the web or database backup feature), and that you want this export to be in one of the common export formats - CSV, TXT, XML, spreadsheet... (Whether that's accurate or not, you'll need to specify that sort of thing.) Give them details and an example sufficient that they can interpret what you want. Draw pictures and email them, if needed. Pictures are worth a thousand words...
I would leave out mention of why you want this. Any programmer can imagine all kinds of uses, and I suspect they'll think like I do, that your data is safer backed up on church servers than anything the average private individual can do (unless you're into engraving gold plates). (Even if every now and then someone's profile has to be restored from backup.) The point being, this part wouldn't impact the requirements for building the feature and is a distraction, so don't mention it.
NOTE: If you want a format that some future version of GL, you'd better mention you want them to build a corresponding import feature. If you want a format some similar app by a third party can import, they can't give you that, so don't even mention it (the third party would have to design an import that reads GL's export (should such a thing ever get built)).