The Burlington Route (CB&Q) was a railroad formed in the 1800s by the merger of small railroads in the upper midwest, some which traced their roots back to 1849. It took its name from Burlington, Iowa on the Missisppi River. Over time the CB&Q grew into an expansive system stretching from Kentucky to the Rocky Mountains, and ultimately to the Gulf Coast through a subsidiary line.
As early as 1901 the CB&Q had seeked to merge with several other large northern railroads, and that goal was finally accomplished when the Burlington Northern (BN) was formed by the merger of the Burlington Route, Great Northern, Northern Pacific and Spokane, Portland and Seattle in March 1970. The railroad was based primarily in the northwest United States, stretching from Chicago to Seattle. If I recall correctly, the BN was the largest railroad in the U.S. at the time of the merger but I can't recall if that was measured in miles of track, value of assets, or tons of freight hauled.
The Burlington Northern Santa Fe was formed in the latest round of railroad mergers in 1995 when the Burlington Northern merged with the Atchison, Topeka and Santa Fe Railway, a similarly large railroad which was based primarily from Chicago to Los Angeles.
Here's more on some of the predecessors of the BNSF: http://www.bnsf.com/about_bnsf/html/history.html
If you modeled the proper transition era (1970+ or 1995+) you could very plausibly include two of the paint schemes. But not all three together. There may have been some CB&Q freight cars which keep their paint until 1995 (if so, they'd be very rare and none that I've seen), but none of the Burlington Route locos keep their paint scheme nearly long enough to see the formation of the Burlington Northern Santa Fe.