Is this the one on this site, the one with the heart? I have not made it but I've done a little DK and I agree the written instructions it gives for row 2 don't seem to jive with the chart of row 2. I have not done much DK (one potholder, and 2 hats done in the round) and the recent stuff was in the round. I don't understand how the edge stitches that you slip work into the chart. I did a practice piece recently doing flat DK and I just used what would usually be the first knit on the chart as the slip stitch and then purled the next stitch (so those 2 steps would be 1 stitch on the chart). Then at the far end for the last stitch on the chart I knitted one with the color shown and then what would be the final purl I worked with both colors. It seems the way I did it wouldn't need extra stitches. The chart has 29 stitches but they say to cast on 30 (60) so they must not include the slipped stitch on the chart. :shrug:
Since my recent work was in the round I read the chart from right to left all the time, but I suppose for flat you have to read every other line backwards like you do with other flat charts. I also think you would have to reverse the colors. So that if the chart shows red as the first knit stitch you would start with white and do the purl in red. I'm not 100% sure about that, but a little experimentation would tell you the facts on that question.
As far as making this potholder go, if you understand how DK works I suggest just following the chart and ignoring what it says about row 2.
Good luck. The member, Of Troy, here at KnittingHelp is good at DK and you could maybe send her a private message and ask her for help if this isn't enough to get you going. I don't think she would mind.