It is true that hydrazine is highly toxic and explosive, but it has tremendous energy density. The decomposition of hyrazine into hydrogen and nitrogen gases AFAIK produces enough heat to ignite the resultant hydrogen when it occurs in the presence of air. But to make it useful for low speed, subsonic jet propulsion would involve tightly controlling the decomposition and combustion processes. Is this possible? And has there been any attempt to design jet engines that use it?
A quick look into wikipedia (https://en.wikipedia.org/wiki/Energy_density) shows hydrazine (in full combustion to N2 and H2O) at 19,5 MJ/kg while Jet-fuel is listed at 43 MJ/kg.
So => no
Hydrazine is sometimes used to power an APU (e.g. for the F-16). APUs are generally turbine engines, so hydrazine turbines exist.
For rockets, there's a movement away from hydrazine and other nasty propellants toward less toxic alternatives. There's little chance aviation will move in the opposite direction.