"High" Capacity Constant Current Chip?

It's hard to give guarantees ... but I can't think of a commonly used circuit where it wouldn't work.

Basically if the output uses transistors they won't share, but if they use FETs they will.

It is all to do with the different temperature coefficients of the two devices. With a FET the hotter it gets the higher is it's resistance, a positive coefficients, so if you have two FETs and one is taking more current the on resistance increases and it takes less current so they share.

With a transistor it has a negative coefficient, the hotter it gets the lower is the resistance. Therefore when one transistor gets more current it gets hotter and so draws more current. Having the transistors closely coupled thermally can help mitigate this to some extent.