Is it permissible for a financially able person to benefit from a free Hajj campaign designated for the needy?

If the donor for a Hajj campaign explicitly states that it is for the poor and needy, and this condition does not apply to you, then it is not permissible for you to perform Hajj through this campaign. This is because the condition set by the donor is to be honored, provided it is lawful. Hajj is obligatory for Muslim men and women when the conditions of capability are met.