|An old image from my black undercoating days.|
Looks to me like the sequence of events (barring all the pre-battle maneuvering) was something like this:
The Anglo-Hanoverians* deploy in line, with the cavalry on the wings. The guns are awkwardly deployed on the right of the infantry wing on a low rise. Whether this rise was a significant feature I cannot tell and there is no mention of it in the sources I have so far read.
The Jacobites advanced in two large bodies either side of some marshy ground which encumbers the centre of the battlefield. A third body of troops under the Prince formed a reserve behind them.
Is this the origin of reports the Jacobites advanced in a mass, the centre retarded by the marshy ground so their “line” formed a “V” with flank attacks going in first?
The Anglo-Hanoverian artillery was not effective. The Dragoons were static; their only contribution was to fire some mounted volleys at the Jacobites as they came on.
Whatever the reason, the Dragoons in the front line broke on contact and fled. I would surmise that the Jacobite reserve effectively pinned the Anglo-Hanoverian centre whilst the large bodies on the left and right simply collapsed the Anglo-Hanoverian line.
There you go - Prestonpans in a nutshell.
*Yes, I read Duffy's "The '45"