New flooring in kitchen
Here is my take on this.  If your cabinets are a standard size and they aren't on legs there is no reason you should remove them for a flooring upgrade.  Even if the cabinets were replaced they should be able to adjust the toe-kick to where it currently is to overlap the new floor.

Notes:


It is a MUST to move cabinets if they are on legs.  You cannot have a seam of old flooring visible.
You need to get the new flooring under the fridge.  It is too heavy and if you leave old flooring under it and need to move it the lip will probably damage new floor.
I would suggest putting it under stove for same reason.  Unless your stove has a completely flat top - most don't and have ridges, the addition 3/8" will probably be completely unnoticable as the heights already didn't align.  I personally like my stove slightly higher so things I am doing on counter don't just slide onto (hot) stove.  From a technical standpoint you can install flooring until legs of stove but like fridge you may have issues with the lip if stove needs to be moved.
There is no reason to have flooring under dishwasher.  They are light and have adjustable legs.  You really want your dishwasher sitting as high of the floor as possible too.  The dishwasher is only removed for major repair and extra height just makes that harder (or it could possibly prevent it from fitting to counter).
If an island is permanent we never floor under it (as we would just damage flooring securing island) if it is floating, we floor it.


For the most part I wouldn't even think of removing cabinets.  I like doing things in a long-term way and people can make a point that flooring should be continuous but after demoing and remodeling 20-30 kitchens I have basically put in new cabinets and never once had to worry about flooring unless I was removing a peninsula or something like that.  It is just not worth the money, the effort, and the potential damage to the cabinets.  Now if you are trying to get new lowers, now is the time.