Halley's comet's next perihelion will happen around mid 2061.
Considering, that its orbit is retrograde (viewable here), is it possible to build a flyby trajectory by means of gravitational maneuvers around the planets and moons?
Yes, based upon what was done for the last time Halley's comet came by.
Fifteen burns of Suisei's 3 N motors during the period of April 5–10, 1987, yielded a 65 m/s velocity increase for a 60,000 km Earth gravity assist swingby on August 20, 1992, helped it establish a Heliocentric orbit around the sun.
Also see Halley Armada https://en.wikipedia.org/wiki/Halley_Armada