Keep in kind that a regiment’s list of battle honours are not inclusive of every engagement in which the regiment was in action. They are the ones selected by the Regiment against the terms and conditions established in the appropriate Army Orders following each War.
For example, for the Second World War:
Participation in Operations
12. A battle honour will not be awarded merely because a unit was present in an operation. To qualify, the unit must:
(a) have been committed in the locality and within the time limits laid down for one of the individual operations defined below; (the full listing of possible Second War battle honours was included in the Army Order)
(b) Have been actively engaged with enemy ground troops;
(c) have taken a credible part on the operations;
(d) be proud of its part in the operations.
As for the Engineers hypothetically having a potentially busier flag [Colour] than other regiments, there were also strict guidelines on how many battle honours from each war could be emblazoned on a Regimental Colour:
… the list of Honours for the Great War for emblazonment on the Colours may not exceed ten, …. - Conditions for the Award of Battle Honours for the Great War 1914-1919, General Orders, 1 Feb 1928
Limitation of Honours to be Emblazoned.
Para 17. A maximum of ten Second World War honours, either battles, actions, engagements or theatres, may be emblazoned on the colours or appointments. - 33-1 Battle Honours – The Second World War, part “A†Supplement to Canadian Army Orders, 10 Sept 1956
2. (a) not more than two battle honours may be emblazoned. These may be either the theatre honour “Koreaâ€, with approproiate year-ends dates added, and one other, or two named operaions; ….. - 33-1 Battle Honours – United Nations Operations – Korea, part “A†Supplement to Canadian Army Orders, 31 Mar 1958
Mike