The course of the Withywindle is difficult to establish, because what evidence we have is somewhat contradictory. The large scale map of the Shire in The Lord of the Rings shows a part of the river in detail, flowing in a distinct south-southwest direction to meet the Brandywine. Approximately the same direction appears on the larger scale map of the same region, with the Withywindle rising within the northern Old Forest and flowing southwestwards through the trees.
In The Fellowship of the Ring I 6 (The Old Forest, Merry states that the Withywindle '...comes down out of the Downs and flows south-west through the midst of the Forest'. This matches the maps in terms of direction, but disagrees on the source (it's later confirmed that the river flows into the Forest from the Barrow-downs, disagreeing with the map). This is problematic, because the Downs lay to the east of the Old Forest, so if the river did indeed flow southwestwards for its entire length, its source could not possibly be in the Barrow-downs.
Later references seem to suggest that the river flowed east-to-west (later in the chapter quoted above, the Hobbits find themselves on a path along the river towards its source, and that path is described as going eastward, not northeastward).
Later maps (for example the colourful map created by Pauline Baynes with input from Tolkien) account for these discrepancies by giving the river a much more westerly direction, flowing from the Barrow-downs through the middle of the Forest. In the map for this entry, we have followed essentially the same approach, but with a veer to the southwest on the lower river to match the course shown on the Shire map, as well as Merry's comment that the river ran southwestward. This seems to match all the available evidence, but the exact course of the river is not known with certainty.