My bike has a front brake.

By trial and error I discovered the best method to brake quickly is to apply the front brake to reduce pace and then use my legs by apply back pressure.

is that the best non skid method to brake?

A few observations,

No matter how well I execute my plans I never stop as quickly as I do when using my road bike which has okay but not great rim brakes. Is that to be expected that fixed gear braking is slower than front/read rim brakes?

It feels I'm going to twist an ankle some times. Is that ever going to happen and I should be aware.

If you need to do an emergency stop - squeeze hard on the front brake and shift your weight as far back as possible... pedal resistance a distant third in importance.

tarck bieks need no breaks

Diabloscott has the right idea. The front brake does the majority of the braking on a bike. This can be up to 100%. Squeeze the front brake hard. Slide your butt back and apply smooth back pressure to the pedals. Focus on the braking and being smooth. Practice will help.

Ride Safe,

Joe

I have found that weaving side to side while using my legs to slow the cranks down helps in addition to using the front brake. The situation depends on how fast I am going vs what's going on. 19mph down the road and you hit a yellow light that you know you can't make, I start weaving to help slow myself down. I don't skid, I don't know how to skid, I don't want to skid. One method you can look into is the skip stop. I haven't tried this, so I don't know how effective it is.

On hilly rides with lots of descending I prefer having both brakes on a fixed gear. Obviously your legs are still spinning but they don't have to apply any forward or backward pressure really.

If you have a front brake that's the fastest way to stop. Period.

Your back wheel isn't even on the ground in an emergency stop.

Why not a back brake, too? For trimming off speed, particularly on a long descent, having a back brake too is a good thing.

As others have said, be prepared to get off the saddle and back as you emergency stop. Don't be lazy, be aggressive on braking. Use your arm pressure to resist the forward motion of your body. Keep low.

I skip stop, very good way to slow down. As for OP, I don't have a brake but when I did I used the exact technique you described above and I never had an issue. TenSpeed also has the right idea when he says to weave, it feels a bit easier and it increases your stopping distance. Other than that you seem good to go, knock on wood I've never twisted my ankle riding or felt like I would.