I understand if this comes too close to violating the 20-year rule, as it's at least partially about something that's happening right now. If it's not history-adjacent enough either, too, I'll be happy to remove it. I really do want to know what some medievalists here think of this, though!
TL;DR: it appears to be entirely coincidental.
The company that became King Arthur Flour was originally founded in 1790 as Henry Wood & Company. Through different partnerships and buyouts, it eventually became known as the Sands, Taylor & Wood Company. In fact, it was still so named until 1999, when the name of the company was changed to King Arthur Flour, their flagship product. In 1896, according to the company's own history (more on that in a bit), George Wood (the Wood in Sands, Taylor & Wood, but unrelated to Henry Wood) was in the audience of a musical adaptation of the King Arthur legend, and was inspired to name their flour after King Arthur, to reflect his "purity, loyalty, honesty, superior strength, and a dedication to a higher purpose," which is high praise indeed for milled wheat. The new brand name was introduced at the 1896 Boston Food Fair.
Note: this is from the company's own history here and a marketing blog post here. Obviously this should be taken as apocryphal, but I think we can at least rely on the timing, if not the motivation behind the new brand name.
Robin Hood's corporate history (they are now owned by Smuckers) says that the brand was started in 1909 in Moose Jaw. There's nothing about why they chose the name, but it was the name of the flour produced by the mill as soon as it opened (the Vancouver Daily World, Victoria Daily Times, and the Saskatoon Star-Phoenix contain advertisements for Robin Hood Flour in 1909, but it does not appear prior to that year).
Do remember that the King Arthur legend supposedly takes place in the late 5th and early 6th centuries, while the Robin Hood legend (usually) takes place during the reign of Richard I (1157-1199). To put that in perspective, they are about as close in time to one another as famous Scottish folk heroes William Wallace and James Bond (although...).
There is a tendency (if I may offer a more subjective view) to view bread, particularly homemade bread, as a "medieval" product, something from "Ye Olde Englande", with wheat fields, mills, and wood ovens. While bread and milled flour are far older than England, people do tend to perceive bread as "homey", and this could explain why two different companies used old English legends for their brand names. Perhaps it's an example of convergent brand evolution.