Jay Close is right about modern A36 steel - some of it has oddball recycled content that forms an oxide skin that makes forge welding essentially impossible. Jay also has good advice about technique.
The main thing is cleanliness. Get the scale off the steel beforehand. Pre-shape the steel so the flux has somewhere to go when you hit it. Think of pressing the balls of your thumbs together. They touch at the center first and then outward. In forge welding shaping the steel like this is called scarfing the joint. Get the flux (20-mule team is fine) in place early, at a red-orange heat. Make sure you have a thick bed of coke so that the fire is oxygen starved at the top. Otherwise you will tend to oxidize the steel, and that gets in the way of the weld. Bring the steel up to a yellow heat, but not sparkling white. Hammer it from the center out. It should spit some flux. Don't spend too long hammering it, but wire brush it, reflux it, and get it back in the fire. Repeat.
When welding in a high carbon piece for the edge, remember that the high carbon steel will burn at a lower temperature than the mild steel. Weld at a darker yellow than you think is right.
Just for illustration, think about this: If you take two pieces of mild steel, say 2" square and 1/4" thick, machine them down as fine and flat on one face as you can, polish them, and then degrease them and then place them face to face, they will stick a little. That is the iron atoms cohering at a microscopic level. Put the plates together on an anvil and hit them with a sledge and they will weld at room temperature. The only reason we heat to forge weld is to save us the machining time - the hammering knocks down the irregularities for full surface contact. The heated acidic flux also cleans the oxides off the surface and washes them away. You can weld at an orange heat if everything is clean enough.
You should also make a drift. That is just a long chunk of steel in the shape of the handle, used as a form. For a throwing axe it is a teardrop shape in cross section, tapering down towards the handle end. Once you have the eye welded you can drive the drift in and use it to form the eye properly.
