For reasons that I can't now recall, 1 and 3 squadrons were the first to form. As has been mentioned, 1 Sqn were equiped with balloons, hence 3 Sqn is the oldest 'aircraft' squadron - motto 'Tertius Primus Erit', 'The Third Shall Be First'.
However, like other posters, I understood 2 Sqn to be the most senior squadron when calculated by length of service rather than date of formation.
Thread Creep - When 3(F) Sqn was being presented with a new standard in the 80s I took a photo of a line up of aircraft from 1 through to 5 Sgn on the ramp outside the old Q shed on 3(F)'s site at Gutersloh (Harrier, Jaguar, Harrier, Harrier, Lightning). Many years later, while boring a squadron of air cadets with a presentation on my years of derring do in the RAF I asked them what the link was between the aircraft in the picture.
Quick as a flash, a little hand shot up.
'They all have Rolls-Royce engines?'
'Yes, but that wasn't the answer I was looking for'
'They are all single seat?'
'Yes, but that wasn't the answer I was looking for'
'You've flown them all?'
'Yes, but that wasn't the answer I was looking for'
In the end I has to tell them the answer (1 to 5, in order), but the little philistines weren't particularly impressed
