Here's what Wiki says about her travels and the ownership of Alan Pegler and Bill McAlpine. I've put a couple of sections in italics as they answer the questions raised elsewhere in this topic.
Alan Pegler
Alan Pegler, who first saw the locomotive at the British Empire Exhibition in 1924, in 1961 received £70,000 for his share holding when Northern Rubber was sold to Pegler's Valves, a company started by his grandfather. When Flying Scotsman was due to be scrapped, Pegler stepped in and bought it outright, with the political support of Prime Minister Harold Wilson. He spent large amounts of money over the next few years having the locomotive restored at Doncaster Works as closely as possible to its LNER condition: the smoke deflectors were removed; the double chimney was replaced by a single chimney; and the tender was replaced by one of the corridor type with which the locomotive had run between 1928 and 1936. It was also repainted in LNER livery. Pegler then persuaded the British Railways Board to let him run enthusiasts' specials; it was at the time the only steam locomotive running on the British Railways mainline. It worked a number of rail tours, including a non-stop London to Edinburgh run in 1968, the year steam traction officially ended on BR. In the meantime, watering facilities for steam locomotives were disappearing, so in September 1966, Pegler purchased a second corridor tender which was adapted as an auxiliary water tank; retaining its through gangway, this was coupled behind the normal tender.
Pegler had a contract permitting him to run his locomotive on BR until 1972. Following overhaul in the winter of 196869 Harold Wilson's government agreed to support Pegler running the locomotive in the United States and Canada to support British exports. To comply with local railway regulations it was fitted with: a cowcatcher, bell, buckeye couplings, American-style whistle, air brakes, and high-intensity headlamp. Starting in Boston, Massachusetts,[19] the tour ran into immediate problems, with some states increasing costs by requiring diesel-headed-haulage through them, seeing the locomotive as a fire hazard. However, the train ran from Boston to New York, Washington and Dallas in 1969; from Texas to Wisconsin and finishing in Montreal in 1970; and from Toronto to San Francisco in 1971 a total of 15,400 miles (24,800 km).
Government financial support for the tour was withdrawn by Prime Minister Edward Heath's Conservative government in 1970, but Pegler decided to return for the 1970 season. By the end of that season's tour, the money had run out and Pegler was £132,000 in debt, with the locomotive in storage at the US Army Sharpe Depot to keep it away from unpaid creditors. Pegler worked his passage home from San Francisco to England on a P&O cruise ship in 1971, giving lectures about trains and travel; he was declared bankrupt in the High Court in 1972.
William McAlpine
Fears then arose for the engine's future, the speculation being that it might remain in the US or even be broken up. After Alan Bloom made a personal phone call to him in January 1973, William McAlpine stepped in and bought the locomotive for £25,000 direct from the finance company in San Francisco docks. After its return to the UK via the Panama Canal in February 1973, McAlpine paid for the locomotive's restoration at Derby Works. Trial runs took place on the Paignton and Dartmouth Steam Railway in summer 1973, after which it was transferred to Steamtown (Carnforth), from where it steamed on various tours. In December 1977 'Flying Scotsman' entered the Vickers Engineering Works, Barrow-in-Furness, for heavy repairs, including an unused replacement boiler.
In October 1988 Flying Scotsman arrived in Australia to take part in the country's bicentenary celebrations as a central attraction in the Aus Steam '88 festival. The event organisers had been interested in having LNER A4 No 4468 Mallard visit, however due to the 50th anniversary of 4468's world record high speed run it was unavailable and 4472 was recommended as its replacement. During the course of the next year Flying Scotsman travelled more than 45,000 kilometres (28,000 mi) over Australian rails, concluding with a return transcontinental run from Sydney to Perth via Alice Springs in which it became the first steam locomotive to travel on the recently built standard gauge Central Australia Railway. Other highlights included Flying Scotsman double-heading with New South Wales Government Railways Pacific locomotive 3801, a triple-parallel run alongside broad gauge Victorian Railways R class locomotives, and parallel runs alongside South Australian Railways locomotives 520 and 621. Its visit to Perth saw a reunion with GWR 4073 Class Pendennis Castle, which had been exhibited alongside Flying Scotsman at the 1924 British Empire Exhibition. On 8 August 1989 Flying Scotsman set another record en route to Alice Springs from Melbourne, travelling 679 kilometres (422 mi) from Parkes to Broken Hill non-stop, the longest such run by a steam locomotive ever recorded. The same journey also saw Flying Scotsman set its own haulage record when it took a 735-ton train over the 490-mile (790 km) leg between Tarcoola and Alice Springs.
Flying Scotsman returned to Britain in 1990 and continued working on the main line until its mainline certificate expired in 1993. 4472 then toured preserved railways. To raise funds for its upcoming overhaul it was returned to BR condition with the refitting of the German style smoke deflectors and double chimney, and repainting in BR Brunswick green. By 1995 it was in pieces at Southall Railway Centre in West London, owned by a consortium that included McAlpine as well as music guru and railway enthusiast Pete Waterman.