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My employer has just told me that the mileage rate they will use is based on an AA chart 2013 Petrol car operating costs estimated on 14,000km per year for first five years of ownership. They are using the line that says "Flexible Running cost per km which is shown as 28c per km. My reading of this chart says that this is essentially the fuel and basic running cost element only and does not take into account the registration, repairs and maintenance, etc etc. Can you please tell me what would be a fair rate for a 2007 Mitsubishi Lancer 2.4l station wagon

You are correct, the flexible costs are fuel, oil, tyres and R&M, but not annual relicensing, WoF, insurance, and most significantly, depreciation. The total running cost for a 2.4 litre vehicle is 78.8c per km, although this is based on a newer car than yours (3rd year of age). As an approximation, the total running cost of your vehicle would probably be around 50c per km as it has depreciated further than a 3 year old car.
However, our running costs are calculated to give motorists an indication of the cost of running their car. Any employer/employee reimbursement is a separate negotiation between the parties, however the AA rate is often used to give each party a platform on which to base any discussion.