Indulgence is still a method of getting onto a military flight but there are very few locations that you can feasibly fly to these days unless your timing is amazing and you have funds available to sort yourself out if the MOD cannot gurantee the plans.
As for ex-military it ids open to serving soldiers and their immediate families. I do know of an ex-soldier that used the system but he was working as a civil servant and arguable got to do it by virtue of that.
A few years back I was doing six months porridge down in the Falklands and Mrs Sartorius tried and failed to get an indulgance flight to join me for Christmas. So she pitched up to Brize Norton in her TA uniform. The conversation with the mover went something like this:
"I'm here for my flight to The Falklands."
"Sorry ma'am but you are not on the manifest"
"I'm hardly likely to be going there for fun am I?"
"Agreed, but your name is not on the list."
"That's OK by me. Can I just have your name for when my CO goes ballistic 'cos I didn't catch my flight."
"Ah. I'll see if we have a spare seat."
Bad weather over Mount Pleasant meant the old girl spent an extra week with me before we blagged her onto a flight back home. Something must have happened during that time because nine months later came the patter of tiny feet.
We resisted the tempation to call Sartorius junior Stanley!
Indulgence Flights on RAF Aircraft
Q. Can I book an indulgence flight for me and my family on an RAF or MOD chartered aircraft, such as a trip to Cyprus?
A. All enquiries about booking indulgence flights for service personnel and their familiesshould be directed to the Defence Passenger Reservation Centre, telephone 030 6789 4800. Members of the general public cannot book indulgence flights.
In that way:
Ages ago in Bahrain, working Joint Comms, if you were RAF , and had a friend in the medical section , he could book you to see a Doctor / specialist in Aden. Flights booked accommodation sorted at the what ever that Mil hotel was called and off you went.
Just as you arrived your appointment would be cancelled by 'Pal' so you had time to shop duty
free (which was excellent) and back to your unit.