Hello. Thank you for contacting the Toolset support.
We do not have any official integration with any affiliate plugin but in theory most of the plugin should work fine without any issues.
I suggest you should search for your desired affiliate plugin that offers the feature you want and then you should setup a test site where you can check how it works.
You can setup site build using Toolset using the Framework installer plugin and setup your test site, if you do not know how to do it, please let me know I will setup a test site for you and share you the access details and then you can add your desired affiliate plugin and check how it goes.
I have checked with some popular affiliate plugins, Toolset seems to be not compatible unless we go with customisation.
In case if I go with Gravity forms, WP forms or other forms which are compatible with Toolset plugins, I think I will be in a position to use affiliate plugins
Can you please let me know which forms plugin is compatible with Toolset. Which means, I will use Toolset other blocks but form is through other plugin.
As Shane suggested, you may or may not have to add some custom code in order to achieve the exact function you are looking for. Let us know if you need any further assistance.
There is no affiliate plugin which supports toolset forms directly unless there is a customization needed. I would suggest you to pass it to development team and consider for improvement.