Fielding was from a family of artists. He was named after the Flemish Baroque painter Anthony van Dyck (1599 - 1641) and possibly the American painter John Singleton Copley (probably 1738 - 1815) too. Fielding was a talented watercolour painter. His father, Nathan Fielding (1746/7 - 1819), had exhibited regularly at the Royal Academy and was also a watercolour painter, as was Fielding's brother Theodore (1781 - 1851).
Fielding specialised in large-scale watercolours, for example, 'Ruins of Rievaulx Abbey, Yorkshire' from 1839, now in the collection of the Victoria and Albert Museum, London. He worked closely with his father. They moved to Liverpool in 1807 and then to Wales in 1808. Fielding studied with John Varley (1778 - 1842) in 1810. He exhibited for the first time at the Society of Painters in Water-Colours (later known as the Royal Society of Watercolours) in the same year. He won a gold medal at the Paris Salon in 1824, along with John Constable (1776 - 1837), although he never visited France.
In the last two decades of his life Fielding spent most of his time in the studio reworking earlier compositions and his work became repetitive as a result. His watercolours remained popular with purchasers though and during his career he exhibited over 1700 landscape and marine scenes.