You are in violation of Section 7m of the Flag Code. As you are obviously ignorant of that code, here it is for you to read.
No. Section 7m of the Flag Code authorizes a governor to half-staff the US flag upon the death of a present or former official of the government of the state, or the death of a member of the Armed Forces from that state who dies while serving on active duty.
The President, by comparison, is authorized to half-staff the US flag by proclamation upon the death of principal figures of the US Government and the Governor of a State, territory, or possession, as well as in the event of the death of other officials or foreign dignitaries.
Governors can order the flag to half-staff to honor fallen soldiers from their state (see Public Law 110-41). The change was the result of governor proclamations, like this one from Governor Granholm of Michigan.
Some object to this extension of a governor's authority because they feel half-staffing the flag for every fallen soldier can be seen as anti-war. Some feel that overuse cheapens the symbolic power of half-staffing the flag, traditionally reserved for political leaders.
Rescind your worthless order to lower flags to half-staff for Rush Limbaugh. Aside from him being a bigot and misogynist while he was alive, he also does not meet the criteria for Section 7m.
Respect our existence or expect our resistance.