You should be able to, assuming it uses standard AVC codecs. Have you tried?
You will, of course, need to have the latest version of Quicktime installed on your computer, per the program's system requirements.
I have quicktime ver 7.7.6 which seems to be the latest. When I import the clip, but I get a green square instead of the clip.
What can I check to find the right codec. I convert it on VCL from fLv to mp4
That might be part of the problem. It's almost never a good idea to convert a file -- unless you know exactly what you're doing. Often converting a file produces a video that's even LESS compatible with Premiere Elements.
On the other hand, Premiere Elements can't edit FLVs. Where did this FLV come from? Is this ripped from YouTube or something?
That said, open one of your MP4s in a program like G Spot or Media Info. See what this program says about the file's dimensions, frame rate and, above all, the audio and video codecs the MP4 is using.