Simply put, a second citizenship platform is a platform for second citizenship.
You can infer from context that platform here refers to a kind of company or professional, as it is in parallel with experts, managers, and agents. This is an unusual use of platform, but consistent with that word's sense of a system or program that provides services. As Macmillan puts it,
- something that allows something else to happen
platform for: The funding would provide a platform for growth and development.
The source mentioned in the article, the The 2017 Global Wealth Review (GWR): Worldwide Wealth and Wealth Migration Trends, is paywalled; however, an earlier edition of the report is freely available, and confirms that the platform in question is a type of firm.
According to Nadia Read, head of world residence and citizenship platform LIO Global: “the main reason people apply for a second residence or citizenship is to ensure freedom of global mobility and access, as well as security and wealth protection for their families.“
A second citizenship (or a second passport, by metonymy) is commonly an economic citizenship, one acquired through investment in a country's economy, and undertaken to take advantage of that country's laws or tax regime as compared to one's homeland. It is a type of dual citizenship, a broader term encompassing the holding of citizenship in multiple countries, including where the hold is on the heart as well as the wallet.
So, second citizenship platform refers to firms like LIO Global, Arton Capital or Henley & Partners which advise the wealthy on matters of citizenship and residence, and provide programs through which they can acquire second citizenships.