Not a BA flight , or NABAFWBAFNFWBACF for short

When I use a word,' Humpty Dumpty said in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.

So what is 'a BA flight' ?  Here's the screenshot from the BA website of flights from Kirkwall to London, via other Scottish airports. 
 

The flight from Kirkwall to Edinburgh or  Aberdeen is listed, along with the onward connection. It is possible to book flights from Kirkwall to London through this website ,and BA collect the fare.

And although operated by AN Other ( Flybe is the insignia on the plane)  the flight has a BA flight number

KOI to EDI at 07.45 is BA4060

KOI to ABZ at 07.50 is BA4101

etc etc etc. 

So you might think this is a BA flight.

WRONG

Although it appears on the BA website , BA have collected the fare, and it has a BA flight number  by which you can refer to it, it isn't a BA flight .

A 'BA flight' is one operated by British Airways.

It becomes relevant when you start to get details of online  check-in and if  flights like this appear in a BA itinerary and its possible to check in online, yet BA say the facility is only available for BA flights. All may become a bit clearer over the next week or so .

I think its very misleading but so far ive managed to establish after a series of emails with BA Customer Relations that these flights arent BA flights and they cant tell me if online check-in is available.

So  what can we call them ?

I think they should be labelled 

Not a BA flight with a BA flight number for which BA collect the fare .

or, for convenience,

NABAFWBAFNFWBACF