At the risk of straying very much off topic, the parliamentary train in question calls at the airport only in 1 direction and only on a Sunday at 1219. The last preceding flight to arrive lands about 0930. The first flight after midday departs at 1725. Thus in the best scenario, one either has to wait almost 3 hours after landing before catching an onward train, or one has to arrive at the airport almost 5 hours before one's flight departs.
Description of parliamentary trains can be found at
Parliamentary train - Wikipedia, the free encyclopedia
Train tickets are most certainly for sale (otherwise one could sue the railway company for no longer providing a service), but are of little or no use to people intending to fly in this case. It is possible that most tickets are purchased specifically by collectors - there's a nice BBC feature at
BBC News - On board a real-life 'ghost train'
Numbers of people entering, exiting and interchanging at a UK station are published by the rail regulator at
Station usage
If you sort the spreadsheet by column V (total entries and exits) you will find that Britain's quietest station is indeed served only by a parliamentary train.
Back to the main thread:
While Kidlington might be deserving of a station in its own right, it is extremely unlikely that Oxford airport can possibly justify the expense of building of a station specifically for the airport for at least the next 5 years. Given that Oxford station is not in the city centre, and Oxford generally has good bus services, I find it very difficult to see public transport from city centre to Oxford airport being anything other than a long bus ride.