The DC current is only to support the output load and to make up for loss. This can be measured with a meter.
The AC current has to do with the primary inductance, time and voltage. I have current probes the clip around a wire.
In the horizontal section of a TV the AC current is much larger than the DC current. If you are using the flyback transformer with out the yoke the AC current will be much lower.
Now that I reread the question, you want to know the secondary current. Some transformers has a ground lead (ground for the 20kv). You can put a current meter there. One problem is that the transformer may be very complicated inside and the ground current may be a combination of many different circuits. Many transformers have multiple outputs. 20kv, 2kv, 1kv etc. You don't want to hang a meter on the 20kv wire. A current probe around the wire will work. The secondary is probably not a simple winding. Most transformers I know of use many secondary windings. It is common to have each winding output less than 5kv. You could have four (winding and diode) that adds up to 20kv.
If there is no output load then there should be no current in the secondary. There will be primary current with or without secondary load.
In better TV sets and CRT monitors there is often a load resistor hidden in the transformer. This load helps regulate the output voltage. In this case there will be secondary current but you will not be able to measure it.
If you are trying to measure the current out the 20kv wire then you can measure the current in the bottom of the load.