live Kp index data I need to create an online service displaying latest Kp index.
Where I can take the data? 
The data should be in machine-readable format, i.e. text files, XML, or CGI gateways, for instance. No graphical plots!

I found this:
http://www.swpc.noaa.gov/wingkp/wingkp_list.txt
Is Est. Kp what I need? I compared the data with plots covering several last days and found that kp values in this file are lower that on the charts.
 A: Kp is not really supposed to be a real-time index. The definitive Kp is calculated by GFZ Potsdam, often several weeks after the fact, based on data from 13 fixed magnetic observatories. These do not all report their data in real time.
I believe the wing_kp data you linked to is a model based on ACE solar wind data: not actual geomagnetic measurements.
Various institutes try to present flavours of 'quicklook' Kp. These are all based on near-real-time data from different subsets of observatories. Quicklook Kp values are mutable: they will change during the course of a 3-hour data-gathering period and may well change as more observatories report their data.  
Also, the data format is not brilliant for computer reading: 
140601  1- 0+ 1- 1o  0+ 1- 0+ 1-    5-      3 0.0

GFZ do provide quicklook Kp to the public in tabular form. You may be able to get the data underlying the tabular data from BGS or SWPC.
You should note that, as you will see if you track them for a while, the different institutes's estimates can vary and will not correlate 1:1 with the actual Kp values once they're published.
All in all Kp isn't actually a very good index for real-time monitoring of the state of the magnetosphere... but it does have a very long legacy so getting something more appropriate adopted is difficult.
