Well first off, even if we knew nothing else about it, we can deduce the Panama-US FTA makes tax evasion easier, not harder, by the leaks of how many companies and individuals are using it specifically for tax evasion purposes. And free-trade agreements don't remove all barriers, you're right about that, but they never increase barriers either. Governments can and still do use protectionist policies to protect local industries for the sake of employment, and limit exports of important natural resources, but by their very nature, the purpose of FTAs is to remove barriers, not enact them.

But going into specifics, it's never the removal of one barrier that makes tax evasion easier. In the case of the Panama-US agreement as it would apply to my ELI5 example, the scheme would be made possible by Articles 3.3 and 3.8, which remove both import and export restrictions, as well as tariffs on those imports, keeping both nations from creating any new restrictions/tariffs and requiring them to gradually remove the existing ones based on an agreed upon schedule.

Article 5.2 requires both countries to speed up and simplify the customs process, making it faster and easier for material goods to flow from one country to the other without too much inspection and oversight, while Article 10.8 requires financial transfers to be allowed to proceed freely and without delay between the two countries.

Taken all together, along with some of the other provisions for removing barriers for financial investment and service providers, they allow companies to carry out the exact kind of scheme I described previously, without any oversight from either country into what either ACME or Seashells is doing, because taking such action in the absence of strong evidence like the Panama Papers, could be cause for complaint from the other country that they are violating the agreement's provisions. And that's something that's taken very seriously.