I agree that there are no "official rules" in the public domain. However, various efforts at unofficial rules have been made. Various Amazing Race-related websites have contained rules. Here is a set of rules from Wikipedia:
Rules and penalties
All teams must abide by the rules set at the beginning of the race. Failure to do so can result in time penalties, which can negatively affect finishing position in that leg of the race. In a non-elimination leg, if the last team to arrive at the mat is checked in before a previous team has completed its penalty, then the remainder of the penalty time will be waited out at the start of the next leg of the race, beginning at the departure time of the next-to-last team.
While the complete set of official rules has not been released to the public, certain rules have been revealed during the various editions of the race:
[edit] Rules
Unless otherwise stated, such as during Roadblocks, team members must stay within twenty feet of each other and stay close to their assigned camera and sound crew. When using any form of transportation, unless otherwise stated, teams must be able to travel with the camera crew. Teams are recorded requesting only two tickets after they have made their initial request for four.[19]
Teams are required to purchase economy class airfare when they fly, using the credit card provided by the show.[20][21] Teams may ask the airlines before or during flight to upgrade their tickets to first or business class as long as they only paid the economy fare.[22] Teams may use their cash stipend to purchase first-class fares for other modes of transportation.[23] Teams may be forbidden from flying on certain airlines or restricted to specific airlines in some cases.
Teams are forbidden contact with friends, family, and acquaintances during the Race, though the Race may provide them with an opportunity to make contact at select times.[24] Unless otherwise stated by the clues, teams are allowed to use the help of locals for navigating and during tasks. Teams are required to have any locals who appear on camera sign release forms that legally clear the footage for use; some teams have avoided or reduced contacts with random local strangers because the release process can take a very long time to complete.
Teams are free to work together at any point unless otherwise stated by the rules.[25][26] Excluding the use of the Yield and U-Turn, teams are forbidden from hindering the performance of other teams such as by taking extra clues from a clue box, taking another team's assigned vehicle, or altering the equipment for other teams at a task.
Teams are forbidden from possessing maps, guidebooks, cell phones, personal digital assistants and other similar aids at the start of the Race, but may use the provided money to purchase these as they progress. These may be provided by the show if required for a certain task.[27]
Teams are not allowed to use their personal items to barter for services on the race, though they are not necessarily forbidden from selling them for cash. The teams' bags may be subject to review during Pit Stops by production. Teams are free to sell or barter any items they have purchased during the course of the race.
In cases where teams are instructed to walk or drive themselves to a destination, teams are not allowed to hire a taxi to guide or take them through the route. In early seasons of the American series, teams frequently employed this tactic; several exchanges of dialogue in Season 17 indicate that this is now forbidden.
Teams are expected to keep the Race fanny pack containing their cash, passports, clues, and other documents with them at all times. Teams that do not have these upon check-in at a Pit Stop are required to go back and retrieve the pack and any missing mandatory contents (e.g., passports) before being checked in. Teams may check in after losing or abandoning any non-mandatory items (e.g., items of clothing), but they must continue the race without them.
Teams must complete each challenge as specified by the clues given to them throughout the Race. Should a team fail to properly complete a challenge, violate any provisions made in a clue or task description, or miss a clue altogether (unless specifically allowed to do so, e.g., by winning the Fast Forward, or by using an Express Pass), they must either go back to the location of the challenge and complete the challenge, or incur a penalty when they check in (see Penalties and time credits below).
Teams are prohibited from begging where it is illegal. On the U.S. version, teams are additionally prohibited from begging at US airports.
Racers may not smoke on the Race.
Teams are required to abide by all local laws of the country in which they are racing.
The teams are often given additional rules and instructions that apply specifically to a given leg or to a task supplied with one of the clues; these are usually not explained to the viewer unless they affect the Race results.
Another source of unofficial rules is pages 12 and 13 of the book "Circumnavigating the Globe: Amazing Race 10-14 and Amazing Race Asia 1-3," which is similar to "My Ox is Broken" (which itself has another set of rules in pages 21 - 25).