Does China use or have any plans to use their Flankers to deliver nuclear weapons like the Americans and the Israeli's do with their F-15's ?
Extremely unlikely since Chinese nuclear policy is to treat nukes as last resort strategic weapons rather than tactical alpha strike weapons, as the likes of the US and USSR did since they he Cold War.
China has a very small nuclear arsenal dominated by high yield strategic warheads. What tactical warheads it does have would be primarily deployed by cruise and shorter ranged ballistic missiles, rather than freefall relying on deep penetration strike fighters.
In that sense, any Chinese asset able to deploy Chinese made long range cruise missiles should also be nuclear capable.