my worcester boiler 28i junior greenstar is firing for a few mins only?

If the brithish gas engineer says the flue is faulty then he should have certified the boiler as 'immediately dangerous' and disconnected the boiler so it is not able to function.
Sounds more like an air lock since he has changed the heat exchanger hence the boiler is going out on thermostat so quickly.
Get on the phone and get british gas to put it right

boiler bill
March 2011