What kind of kites are you transporting? And, are you trying to get by without paying the extra baggage fee?
I'm a cheap traveller, so pull the rods out of my Revs and put them into an inexpensive fly rod case. That becomes a carry on item ... same class as the book you carry on to read. Some simply fold their Rev sails and place them in their checked bag ... I like to roll them around 2~3 inch diameter foam tube to prevent some creases.
For the additional soft foil kites, I use a compression sack ... last trip had a 100 sq ft foil, a 20 sq ft foil, three 5 sq ft foils, two 35-foot banner tails, two tube tails, and an assortment of flying lines, sand anchors and misc stuff. My compression sack is sized to be my main carry on piece. If it doesn't fit in the overhead ... I release the compress straps and reshape it to fit.
Rev handles, stakes, and other questionable items go in my checked suitcase with the Revs and my cloths.
This has worked for several one week trips without paying an extra baggage fee. Of course, if you fly in excess of 100,000 miles a year, then you're not worried about these steps.
Cheers,
Tom