By "notes" I presume you mean emails, is that correct?
When you first installed the BTMail app and if you had set the BTMail app as a POP3 account and had not selected to "leave mail on the server" when you used the app, your emails would have been downloaded onto your device and once they were downloaded they would have been deleted from the BT email servers.
Once they have been deleted they are not recoverable from BT.
When you deleted the BTMail app on your iPhone and then reinstalled it the "new" installation would try and download any emails that you had on the BT server but if you have done as outlined above there would be no emails to download because the had been deleted from the server.
You may be lucky that the folder that the emails were stored in is still on your iPhone and if you can locate it you should be able to recover the emails from the iPhone.
I do not use either an iPhone or the BTMail app so I am unable t assist where you may be able to locate the folder.
If on the other hand you set the BTMail app as an IMAP account the app is synchronised with the BTMail servers and what you see in the app is what is on the BT email servers.
If the emails are not in your BTMail app they will not be on the BT servers and if they are on the server they will be showing in the BTMail app. If they are not there they have somehow been deleted.
You may be fortunate and they may be in the Trash folder but if they are not there they will not be recoverable.
