I also need to redo my kitchen floor. At present it has stick on
vinyl tiles that I really hate. Some of the corners have been
chipped so that the damaged areas spread as more traffic goes over it.
Furthermore dirt seems to stick to the tiles.

The compressed type wood flooring looks pretty good. I understanding
that they are "floaters" that is they are slotted-locked in place and
no glueing or toeing with brads is necessary. If this is the case can
I just lay them over the existing vinyl tiles? Peeling of the tiles
to expose the subfloor may mean that I will have to sand the subfloor
to remove the old glue patches.

I also need to redo my kitchen floor. At present it has stick on vinyl
tiles that I really hate. Some of the corners have been chipped so that the
damaged areas spread as more traffic goes over it. Furthermore dirt seems to
stick to the tiles

Of course you need a better floor than that, especially in a kitchen

The compressed type wood flooring looks pretty good. I understand
that they are "floaters" that is they are slotted-locked in place and
no glueing or toeing with brads is necessary. If this is the case can
I just lay them over the existing vinyl tiles?

Sure you can. But let's be logical here.

Peeling off the tiles to expose the subfloor may mean that I will have to
sand the subfloor to remove the old glue patches.

Here's the bottom line: the first flooring job was a hack installation and now
you want to compound the problem by covering it up. Read the instructions that
come with any flooring product and note the first thing mentioned is a decent
substrate. So forget the shortcuts. Get the subfloor clean and level (sealer
and Bondo as needed) and you won't be doing it all over in couple of years.
Good luck.

Joe