My book says (lh)T1,f1,f2,f3 rh f3 little finger rc
but all I get is an F
It cannot be the flute surely...it must be something i'm doing wrong
Anyone care to help?
Your book is indicating the correct fingers. Actually, it certainly CAN be the flute.
It's often difficult to diagnose problems remotely, but there are a number of things that could prevent the F# from playing while the other notes play just fine. The most likely possible causes are that the spring on the F key is either broken, bent, or unhooked or the RH mechanism could be binding.
But, let's try an easy remote diagnosis:
Don't attempt to play the flute, but hold it so that you can observe the right hand mechanism.
Close LH1, LH2, and LH3 and then watch as you depress RH3. As you do that, watch the 3 keys above the RH3.
You should see the third key away from RH3 go down when you press it. See photos below.
My guess is that RH1 is also going up and down too as you press and release RH3. If so, it should not and that is why you are unable to play F#. If that is what you see, then you need to get a flute repair technician to check it. If it is simply an unhooked spring, the tech should be able to easily hook it back on the spot. If there is a broken spring or binding mechanism causing it, then that repair is more involved and will require the tech to disassemble the RH mechanism to resolve the problem.
With RH3 open:
Normal - RH3 pressed - only 1 other key should close
This indicates a problem. RH3 pressed - RH1 is also closing. Compare to previous photo.
Let me know what you observe.