Hello,
thank you for you question!

The National Center for Home Food Preservation is the trusted source for research-based tested recipes, endorsed by the USDA, and recommended by Ohio State University Extension. Starch interferes with heat transfer during processing. Flour (contains starch) is a forbidden ingredient in canning because it alters the thickness or density of the final product which effects how long it takes for the food being processed to reach a safe temperature in the core of the jar. Therefore, it is not recommended to use flour to thicken soups, relishes, or pie fillings when canning. 

In reviewing the recipe you provided ½ cup flour is an ingredient. I followed the recipe source provided in the link and the information commented on exceptions to the recipe using flour as a thickener if the recipe has been “lab-tested for safety”. I then followed the “lab-tested for safety” link that points out Penn State Extension states to never add thickening agents to a home canned product and then that Penn State Extension acknowledges that “…the use of thickener is fine when a tested recipe calls for it.” Healthycanning.com then shares a list of tested recipes as of 2015 using flour and corn starch. Of the three recipes under flour, two are not from the USDA. The third recipe cited, Pickled Corn Relish, is a USDA tested recipe in which, after simmering, a flour paste of ¼ cup of flour is blended in ¼ cup water and stirring frequently is an option (recipe link below). 

The Thousand Island Relish recipe you shared from healthycanning.com states it is tested by Bernardin a company that maintains its own safety test labs and personnel. I am not able to verify the published science behind the relish recipe outside of this claim. Once again, we recommend using tested recipes from the NCHFP. There are several relish recipes provided on the NCHFP website and you can find one that has similar ingredients to try in place of the relish recipe shared. Please refer to the resources below for more information and recipes. If more information regarding the science behind the recipe becomes available I will post it.

Resources to review:

Penn State Extension: Foods that are Not Safe to Can

https://extension.psu.edu/foods-that-are-not-safe-to-can

Ohioline - Food Preservation: Canning Soup and Forbidden Ingredients: 

https://ohioline.osu.edu/factsheet/hyg-5340 

National Center for Home Food Preservation: 

https://nchfp.uga.edu/; https://nchfp.uga.edu/how/pickle

https://nchfp.uga.edu/how/pickle/relishes-salads/pickled-corn-relish/ 

USDA Complete Guide to Home Canning:

https://nchfp.uga.edu/resources/category/usda-guide

https://nchfp.uga.edu/resources/entry/guide-part-6-fermented-food-and-pickled-vegetables