Same problem I get when trying to use that clip.
I always get one nand easy, and the other is a pain.
I think I need to modify the clip more. Like in the pics in baileyscream's guide
Also do this:
The biggest pain by far of the whole process was getting that solderless clip on correctly for WinSkeet to recognise it. I would add that gently scrubbing the pins with some cleaning Alcohol on a clean toothbrush (on the solderless clip and NAND chips) can help in making sure it's won't fail due to the pins being dirty (as that was the case with my solderless clip).