SS taxes are paid based on individual earnings. If you are employed you pay half and the company matches. If you are self employed, you pay the full amount. Thus, in Trump's partnerships, he is considered self employed. He therefore pays roughly 15% in SS taxes on his share of earnings paid to him by that partnership. For his C corps, he pays roughly 7.5% on his salaried earnings, but if he owns the company then his company matches, which means he and his company pay the full 15%. If he has multi-member LLC's they are treated as Partnerships and he pays the full 15% on all LLC income attributed to him.
Again, not sure how you can conclude he pays no SS taxes, unless all of his companies lose money.