I emailed support but their reply didn't make sense. They gave instructions on how to move files from dropbox to iCloud, but no way to back up what is on the phone. I replied, but haven't heard back from them yet.
Here is their initial reply to me which doesn't answer the question at all:
Oct 6, 11:47 MST
We had to switch to iCloud because Dropbox changed the way there system worked so we no longer could use it. I have attached the article from our site about how to move your data over from dropbox to iCloud: https://help.ibird.com/hc/en-us/articles/115007450248-My-Apple-Favorites-Disappeared-after-I-Updated
Sometimes the species will show up as their number in our system and not their name, so I have also attached the article with the spreadsheet that has the specie's corresponding name with their number: https://help.ibird.com/hc/en-us/articles/115000654052-Migrating-Favorites-and-Notes
Thank you for using the iBird app, and please let me know if I can be of any additional assistance,
The first article isn't on point at all since there is no apps folder in my dropbox directory and it didn't answer my initial question
The iBird journal backup files in dropbox get saved with filenames such as iBird Journal Backup 4-3-17.journal. These are cool as the jpg files that I attach to my sightings are part of the embedded database. I was able to get around the issue with my iPhone. I chose the backup to email function and used Apple's "Maildrop" system to send and receive the large file.
If you have an iPhone, this will work, as long as your database is <5 GIG. If you have a different phone and a database <25 Meg, a normal email will work, otherwise you can probably use a Google Drive link.