Hi Steve,
I don't know of any standards for park gauge trains per se. That's not to say none exist - only that I cant recall recent discussion directly associated with flange or rail wear standards.
I've sent a couple of emails to a couple of park gauge experts, asking them about your inquiry. Hopefully one or more can comment here.
So, independent of that, three resources that might be useful for followup are:
IAAPA - the amusement and attractions industry association,
Tourist Railway and Museum Association, now rebranded as Heritage Rail, or
State amusement certification agency for whatever state you are interested in.
Here are the web sites for the two trade organizations.
http://www.iaapa.org/
https://www.atrrm.org/index.php/about-us
Back in the 1920's the amusement park industry standardized all park train rides on 24" gauge, and published equipment and maintenance standards. This was an effort to standardize the many smaller gauges, to establish cheaper, more cost effective purchasing of railroad parts and rail - particularly wheels and couplers - costly wear and tear items for park gauge operators. Also to establish best practices for park gauge train maintenance and operations. 24" ga railways were the upper limit gauge exempt from the old United States Railway Administration (USRA) common carrier rail regulations. Anyway, IAAPA might be the keeper of any current equipment and trackage standard surviving from the era.
The Heritage Rail web site mentions a publication regarding recommended practices for tourist railroad operations. There may be something useful in this publication that you can use.
Also, most states have some annual inspection and certification authority for amusement rides. Often train rides are included in these departments Responsibility. In Hawaii and Alaska, The state
Department of Labor was the certifying agency.
Further resources might be the Cal State Railroad Museum in Sacramento, Ca, or any other of the national or State railroad museums.
If I hear anything from the people I emailed, will forward to you for review.
Glenn