  Two-dimensional van der Waals materials have become an established platform
to engineer flat bands which can lead to strongly-correlated emergent
phenomena. In particular, the family of Ta dichalcogenides in the 1\textit{T}
phase presents a star-of-David charge density wave that creates a flat band at
the Fermi level. For TaS$_2$ and TaSe$_2$ this flat band is at half filling
leading to a magnetic insulating phase. In this work, we theoretically
demonstrate that ligand substitution in the TaSe$_{2-x}$Te$_x$ system produces
a transition from the magnetic insulator to a non-magnetic metal in which the
flat band gets doped away from half-filling. For $x\in[{0.846},{1.231}]$ the
spin-polarized flat band is self-doped and the system becomes a magnetic metal.
In this regime, we show that attractive interactions promote three different
spin-triplet superconducting phases as a function of $x$, corresponding to a
nodal f-wave and two topologically-different chiral p-wave superconducting
phases. Our results establish monolayer TaSe$_{2-x}$Te$_{x}$ as a promising
platform for correlated flat band physics leading to unconventional
superconducting states.
