First of all, Jackson is not a lawyer, secondly of all Jackson receiving a Cabinet post even under Dellums is borderline ASB. In theory, a VP can also serve in the Cabinet (Byrnes/RFK as de facto, not de jure DPOTUS) but it has never been done because they don't have the time do both jobs at once. You can't run Treasury and preside over the Senate without the use of a Harry Potter Time Turner. 
Dellums will want a more moderate Cabinet due to his socialism.
Vice President: Lloyd Bentsen
Secretary of the Treasury: Hyman Minsky
Secretary of State: George McGovern
Secretary of Defense: Cyrus Vance
Attorney General: Nicholas Katzenbach (IOTL RFK's deputy, successor as AG, former Deputy SecState, Carter's OLC director)
HEW Secretary: Joseph Califano (LBJ's former HHS Sec)
Secretary of Commerce: Robert Strauss
Secretary of Agriculture: Herman Talmadge
Secretary of Labor: Ray Marshall
National Security Adviser: Harold Brown
Dellums will want a more moderate Cabinet due to his socialism.
Vice President: Lloyd Bentsen
Secretary of the Treasury: Hyman Minsky
Secretary of State: George McGovern
Secretary of Defense: Cyrus Vance
Attorney General: Nicholas Katzenbach (IOTL RFK's deputy, successor as AG, former Deputy SecState, Carter's OLC director)
HEW Secretary: Joseph Califano (LBJ's former HHS Sec)
Secretary of Commerce: Robert Strauss
Secretary of Agriculture: Herman Talmadge
Secretary of Labor: Ray Marshall
National Security Adviser: Harold Brown