The tallest tower built by a private individual during the 18th century was probably the central tower of William Beckford's Fonthill Abbey, which was built and rebuilt several times to heights between 200 and 300 feet (60.96 to 91.44 meters) tall. At an early stage Beckford had a design to build a tower about 200 feet (60.96 meters) tall with a conical spire about 200 feet (60.96 meters) tall on top of the tower for a total height of about 400 feet (121.92 meters), but I don't remember the details. And presumably Beckford could have afforded to build the 400 foot design.
Presumably a wealthier institution or government could have built a much taller tower if motivated to.
According to legend, there was a medieval Chinese building towering about 300 meters tall, though killjoy archaeologists believe it was less than half as tall.
See posts 88, 89 on page 9 here:
The Yongning Pagoda was described in Record of the Buddhist Monasteries in Loyang to be 90 Zhang high and 100 Zhang with the spire, or 330 meters (1082.68 feet), but in the commentary of the Waterways Classic "only" 49 Zhang or 163 meters (534.777 feet). Archaeologist Yang Honxun who excavated its foundations believed it was about 147 meters (482.283 feet) tall.
It seems to me that building a somewhat taller and wider and flat topped version of the Great pyramid and then building a somewhat taller version of Yongning Pagoda on top of it might be enough to reach or barely exceed 300 meters height.
Ancient Roman writers claimed that the destroyed tomb of Lars Porsena stood 200 meters tall. Certainly a Roman Emperor could have built a taller structure than the king of a Etruscan city state could have built, but nobody knows how tall the tomb actually was.
It has been suggested that for reasons of prestige Emperor Claudius must have built his lighthouse at Ostia, port of Rome, even taller than the Pharos of Alexandria, which is believed to have been 120-137 meters tall.
18th century architects could have "cheated" by building a tower on top of a hill of stone and then cutting away at the stone hill until it looked like the lower stories of the tower. In The Lord of The Rings The White Tower in Minas Tirith stood 1,000 feet (304.8 meters) above the plain, being 300 feet (91.44 meters) tall with its base 700 feet (213.36 meters) above the plain on the seventh level of the city that was carved out of a conical hill.
Anyway, it seems theoretically possible that a sufficiently wealthy client and a sufficiently brilliant architect could combine to built a structure 300 meters tall or slightly over with 18th century technology.