Why am I failing to connect this simple kitchen sink pipe?
To avoid cross-threading, spin it backwards until you feel it drop into another thread; this is where and when it's lined up. First attach it to the sink and then fight with other connection, leaving everything lose until it's all fitted together. For the fitting you have, turn this picture up-side down: (make sure the grommet is properly orientated)




  The bottom of the drain spout always seals to the drain plumbing using one of these clever conical, or wedge type of gaskets. The nut on top pushes the wedge into the drain pipe, which compresses it and cause it to perfectly seal between the drain plumbing and the spout from the sink. -woodgears.ca


Plumbing is always a can of worms; you'll find new fittings much easier to work with, and the reusing of old grommets to be less than ideal. While you're at it, replace it with a sanitary elbow like it should be. Flexible lines should be avoided if at all possible, but they sure make for an easy install.