There are five probes leaving the Solar System. Pioneer 10 and 11 are no longer functioning. Voyager 1 and 2 are functioning but their cameras have not been used since the early 1990s, and it is unlikely they could be reactivated.
New Horizons has two camera systems. The most powerful, the LORRI system is a 20cm telescope. However, it has a key problem - it can only see about a third of a degree, and to move it you need to move the entire spacecraft. To do that it, you need to use fuel. Searching speculatively for new objects would rapidly deplete the on-board fuel supply, and prevent the spacecraft being retargeted towards new flybys.
There is another camera, Ralph/MVIC, which has a wider six-degree angle and does not rely on rotating the spacecraft, but it is also less powerful and would be less able to make out a small dim object.
If we had reason to go looking for a Planet Nine with LORRI, it might just be on the edge of possibility... if the probe was heading in the right direction and if we were lucky. Current Earth-based surveys have ruled out the possibility of it being any brighter than magnitude 22 as seen from Earth. LORRI's maximum is about magnitude 21. This would mean LORRI would have to be approximately twice as close to the planet as Earth is to have any chance of finding it, even if we knew exactly where it was. This is only really possible if the probe is more or less heading towards it.