Can I fly from Los Angeles to dc with a matricula consular?

Unfortunately no, you cannot fly from Los Angeles to Washington, D.C. with a Matricula Consular alone. A Matricula Consular is an identification document issued by Mexican consulates to Mexican nationals living abroad, and it is not a valid travel document for air travel within the United States. You will need a valid passport or other acceptable travel document, such as a permanent resident card or a valid visa, to fly from Los Angeles to Washington, D.C.