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Yes. However, the only state capitol that flies its state flag with out the US flag is Honolulu, Hawaii
State flags may be flown at the same height as the US flag, unless on the same flagpole. There is an urban legend that Texas' flag is the only one that can be, because it was an independent republic before joining the US, but that is false. There are links below.
AnswerOhio.Ohio.IT IS THE ONLY STATE
No only Texas and Cali
Only US flag to incorporate the Union Flag of Great Britain.
Hawaii
Any state flag should be flown below or level with the US Flag, but never above it. If it is on the same level it should be on the right, this includes Texas. The rumor that Texas is the only state that is allowed to fly at level with the US Flag is just that a rumor and an urban myth.
The USA has its own flag and the United Kingdom has not got a flag
The Burnett flag was the original flag of the Republic of Texas. The Burnett flag duplicated the flag of the Republic of West Florida, but changed the color of the star from white to gold. The design honors the Republic of West Florida as the first "Lone Star State". The Republic of West Florida was illegally annexed by force by the United States government without the approval of congress. The flag of the Republic of West Florida therefore became a symbol of US expansionism and aggression. The West Florida flag became known as the "Bonnie Blue Flag", and was used as a battle flag by the Confederate states during the war for Southern independence. The Bonnie Blue Flag is still in use today by Texas secessionists and other Southerners who favor state's rights and/or secession from the US.
The State of Washington, the only US State named for a President
California
This is a 1845 Republic of Texas flag, the flag which flew over the Texas Republic before it became occupied by the US government.