Rust around gas boiler flue joints

[Madrab]

Leaking inner flue seal at the telescopic joint. Condensate then drips onto the steel outer flue and runs back to the boiler, leaking at every joint.

Yup, do agree and I've seen that before too but looking at pic 1, the water is leaking out of the joint, onto the top of the case and then along and seemingly under the turret, which is apparent from the staining and the rust at the screw hole in pic 2. In pic 2 the water can be seen where it has dripped down through the screw hole in the top of the case onto the top of the inner chamber. That screw hole is beneath the turret, so it looks like it's running under the turret. I'm not saying it is for definite, I'm just saying it should be checked sooner rather than later.

Will it be necessary to replace the whole flue?

Not sure, the flue will need to be disassembled and checked, it may be re-usable, not sure if you can get the seals separately tho.