Any chance that you could post a step by step tutorial on this method?
I'm no expert, but this is what I do.
1. If your lever has a reservoir, remove the cover and top it off.
2. Attach hoses to two clean syringes. Fill each syringe half way and burp the air out of the hoses.
3. Attach the hoses to each end of the brake hose, i.e. lever and caliper.
4. If either end uses zerk fitttings or a bleed screw, open them.
5. Affix one syringe to the bike so that it is vertical, forcing air out of the fluid. I usually use the caliper end.
6. Push the caliper syringe while pulling on the lever syringe. It takes practice, but it's not hard. Push about half the fluid. No syringe should be more than 3/4 full or less than 1/4 full.
7. Hold the lever syringe vertically to burp the air. Push the lever syringe while pulling the caliper syringe. You can also do what
@PedalUma suggests, and pull on the syringe with less fluid first to create a "vacuum", then push the fluid through with the other syringe. If this method works, increase the push force to drive out trapped bubbles.
8. Always make sure that bottom of both syringes are vertical before moving fluid.
9. Repeat 5-10 times.
10. After moving fluid, flick the lever lightly, which can force sticky air bubbles out of the lever.
11. Test the lever for travel and firmness. When it's acceptable, disconnect both syringes and close both bleed screws or attach the covers.
All this assumes that the fluid is good. Changing fluid is similar, but I just use one syringe at the lever end, and put a hose onto the caliper, and put it into a jar. Keep refilling the syringe until the fluid runs clean, then bleed.