whatever you consider safe. This is dependent on experience and the equipment you are using. If it seems very windy i.e. trees are really bending and there are large, heavy gusts, then it is probably too windy for your setup. You generally can always walk away and come back another time.
On the above scale, you would normally looking at around Beaufort 4. Anything above 20mph+, you will need different kites and stronger line and reels. We use these type of kites only under supervision of another member and a lot of luck. High wind kite flying can be interesting, but not recommended until you know what you are really doing.
You can buy devices that measure wind speed for you, but simple observation of the grass and trees moving should give an indication of safe wind speeds at ground level. Above the tree line, the wind starts to increase and the higher you go, the wind will be stronger and generally more constant.
Attached below is a nice image of a Beaufort scale that I like and use.
The kites that we supply have the following manufacturer specified ranges of wind speed: HQ 2m Delta Graphic 5-24 mph HQ 3m Delta Graphic Rainbow 5-24 mph HQ Power Sled 1.7 6-24 mph
As pointed out by Jim, you do have to keep in mind that the wind speed increases with height. This can be a very sharp increase if there are obstructions at ground level.
Too high a wind speed can cause the spars in the sled to pop out and the kite shear at speed out of the sky. This has happened to me but the camera survived ;o)
Too high a wind speed with the deltas could snap the spreader spar but, so far, this has not happened to us and these HQ deltas have the more resilient fibreglass spars.
A few recipients also have the 9ft Mylar delta kite. This kite should be handled with more care as the spars are fibre-reinforced resin, but the spreader is nicely tapered for flexibility. This kite has good flight characteristics and is wonderful for lower wind speeds, but at the present time, it is not being exported to the UK.
For a given kite type, in terms of ease of handling, the stronger the wind, the smaller the kite that should be used. Some kites can partially compensate for wind speed by flexibility, or by flying at a higher angle, or both.
For the kites that we have sent out consider about 20mph a threshold, including transient gusts! The lines with the two larger kites are Dacron which has some give to partially compensate for sudden gusts. Keep an eye on the forecast:link
Increasing wind speeds also extends the range of turbulence around trees and building etc.