I recently came across the following notice in the Salisbury Times of 27th January 1933, under the heading 'Wooton Bassett Flitch Trial': “At a flitch trial held at Wootton Bassett last week, Mr E.C. Fielder was judge and Mr H. Dale, Clerk of the Court: there were also four barristers, all in legal attire. Dr J.M. Ross was foreman of the jury of bachelors and spinsters. Upon the long table in front of the judge were the flitch, two hams, two pieces of bacon and a p[ork pie]. Five claimants were ushered in by the ushers ... and the Sergeant .... The awards were as follow: 1: Mr and Mrs Carter; 2: ... Street; 3: ... Woodward; 4: .... Parsons; 5: ... Hawkins”. So, if you will pardon my ignorance, what was that all about? Clearly it was an award to married couples, and taken seriously if barristers were prepared to be in attendance, but what else? Was it a Wiltshire custom?
To take your last question first, no, it isn't or wasn't specifically a Wiltshire custom. The most celebrated flitch trial takes place in Leap Year at Dunmow in Essex, and the flitch - an entire side of cured pork - is awarded to married couples who can offer evidence of a harmonious relationship. Traditionally the proof was the absence of a cross word for a year and a day, and the earliest references date as far back as 1509 - at Wichnor, Staffs. -, and 1615. A Google search returns thousands of references, of which only the first 80-odd are linked. It seems that there were flitch trials at Barry and Loughor in Glamorganshire, and there is a reference to a trial in Alcester in June 2001 before the Court Leet, where the custom was stated to have been revived for the first time in twenty years. As for where it was held, it is most likely to be held in areas where there is a strong tradition of pig farming and bacon curing, and this certainly applies to north Wiltshire, with bacon curers such as Harris at Calne in the recent past, and an industry represented to this day by Bowyers at Trowbridge and other producers in Lacock and Chippenham.
Google search on: "flitch trial"
Oxford English Dictionary, vol. 5, p. 1066 col. B
Trade and telephone directories, 1939-date