Flickering LED lights
I'm no lighting expert (Russell is the man for lighting) but  I think it's a safe bet that it's the transformer, and the fact that it's designed for halogen lamps.
As far as I am aware, halogen lamps have quite a long time constant (> 1s) so variation in supply will be not noticable unless it's very slow. Contrast with LEDs which have time constants in the nanoseconds and they would flicker.
So for LED driving you need a very smooth supply, which other technologies don't usually need - for instance an incandescent buld can be driven directly from an AC source at a relatively low frequency and you won't notice any flicker due to the long time constant.   

I think getting a transformer specified for LEDs should solve the issue. To confirm there is variation in levels you could test the output with an oscilloscope if you have access to one. Also make sure the cables connecting the lamps are not too long and of a decent diameter (in case there is excess resistance which can cause voltage drops)