I can program the 30 sec skip into my generic time warner remote, but not my Harmony One

How do I do this?

Here is the exact procedure to program a 30 second skip to the remote.

1) Press the "Cable" button at the top of the remote to put it into Cable Box control mode.
2) Press and hold the "Setup" button until the "Cable" button blinks twice.
3) Type in the code 994. The "Cable" button will blink twice
4) Press (do not hold) the "Setup" button
5) Type in the code 00173 (for 30 second Skip).
6) Press whatever button you want to map the skip function to. (I mapped mine to the FAV button)

Doesn't the Harmony One have learning ability? Why don't you use the time warner remote that you already programmed with the 30 second skip function to teach the Harmony the ir signal?

It's already in the database. It is often labeled as advance in the button options.

Since you mapped the cable box skip function to the FAV button on the original remote, then the Harmony button mapped to the "Favorite" command will do the same because it will be sending the same IR command as the FAV button on the original remote. Check the behaviour of the "Favorite" command in device mode, then go into the Activity Customize Buttons and map the "Favorite" command to any desired button.

Note 1: Are you sure you want to sacrifice the FAV button on the original remote? You can use another button, and if its function is not in the device dataset, then simply learn it (as mentioned by Kupakai).

Note 2: Check the device customize buttons to see the device button mapping and don't confuse label names with command names.