Is it possible to create a direct supersonic airflow to a turbofan's afterburner in order to enhance the performance or reduce the fuel consumption?
The J-58 took compressed air from the compressor at stage 4 and piped it directly into the flow aft of the turbine. This cooled the exhaust stream that entered the afterburner, so the starting temperature there was lower and the density higher, which increases efficiency and thrust. Note that the intake of the SR-71 slowed the flow down to Mach 0.4, so all internal flow was subsonic. Only when the hot exhaust gas in the afterburner expanded again would the flow speed increase to supersonic speeds again.

This is only possible because the intake would already compress the air by a factor of nearly 40 when flying at Mach 3.2. This precompression scales with $$p_0 = p_{\infty}\cdot\frac{(1.2\cdot Ma^2)^{3.5}}{\left(1+\frac{5}{6}\cdot(Ma^2-1)\right)^{2.5}}$$
so the precompression is much lower (less than 6) for a typical F-414 maximum speed of Mach 1.8. 

($Ma$ = Mach number, $p_0$ = ram pressure, $p_{\infty}$ = atmospheric pressure).

The gains in efficiency scale with the ratio of starting and exhaust temperatures (measured from absolute zero), so the increase in efficiency is much lower than what you seem to hope for.

Make sure that flow speed at the entry of the afterburner is decidedly subsonic. Supersonic flow at the start of the afterburner section will only delay ignition until the flow exits through the nozzle. All afterburners have rings inside, called flameholders, which cause local separated flow, so some burning gas is always present to ignite the newly arriving fuel-air mixture.