I am sorry I missed your question before.
RFD plays a very important role in arguably most situations in sports and daily activity, where an efficient means of activating muscles quickly, or of producing high impulses within small time periods is more desirable than being able to apply maximal force regardless of the time frame.
"Explosive-ballistic training" can be done in a number of ways, it usually involves lifting submaximal weights (typically 50% of 1RM or less) with sincere effort to produce as fast a movement as possible. "Ballistic" training means doing an explosive movement and actually throwing the resistance implement.
There is an interesting study that indicates there might be some improvement to the neural aspects of RFD even with significantly heavier weights (thus slower movements), if the sincere intention of the lifter is to produce force as explosively as possible, but obviously this would not be the most productive way to train for it.
Reversible muscular action movements done explosively can also be used to increase RFD in relevant movements (i.e. plyometric jumps to increase jumping ability).
If you want to specifically increase your RFD for squats, then the obvious choice is to do explosive submaximal squats, jump squats or even explosive squats with accommodating resistance. Power cleans have the basic element of hip extension (as well as knee extension to a lesser degree) which means there will be some amount carryover, but the entire motor pattern is significantly different from squats (weight distribution is different, ROM is different, no SSC involved, etc.), which means the amount of carryover will not be anywhere near optimal.