Did Brown v Board of Education move forward the development of Special Education Law in the United States (for example, students with disabilities)?

As you answer this question, you want to analyze the results and legal decision of Brown v Board of Education in relation to several elements within the case. Yes, the Brown decision advanced the movement for Special Education laws because the Court mandated that all students have an equal right to quality education.
The landmark decision of Brown v Board of Education declared that segregation of children in public schools was illegal and unconstitutional. "Separate but equal" was deemed to be inherently prejudiced. Much of Brown's argument resided in the rights and protection clauses provided by the 14th Amendment of the US constitution. In relation to later laws regarding special education, the premise that it is unfair to segregate students for any reason was the vital foundation.
The specific Equal Protection Clause of the 14th Amendment was a central focus of the Brown case, as it provides that all citizens have equal protection. This clause has been applied in many cases to give equal access to education to all students of ability or disability.

nor shall any State . . . deny to any person within its jurisdiction the equal protection of the laws

In the Brown decision, the Supreme Court stated

Segregation of white and colored children in public schools has a detrimental effect upon the colored children. The impact is greater when it has the sanction of the law; for the policy of separating the races is usually interpreted as denoting the inferiority of the Negro group. A sense of inferiority affects the motivation of a child to learn.

After the Brown decision, movements began among parents who claimed that any segregation of students based on abilities was also unfair and unequal. Parents began to file lawsuits against school districts when their children were segregated in school from others based on a disability.
Therefore, as this movement for total educational inclusion continued, Congress passed the Elementary and Secondary Education Act (ESEA) in 1965. This federal legislation protected equal access to good education for all students, specifically any disadvantaged.
Just a few years later in 1970, two more cases argued for additional support for any challenged students with special needs. These cases were Pennsylvania Assn. for Retarded Children v Commonwealth of Pennsylvania (PARC) and Mills v Board of Education of District of Columbia. These cases again stated that students with special needs cannot be segregated or ignored.
In the Mills case, the Court declared:

the failure of the District of Columbia to provide publicly supported education and training to plaintiffs and other “exceptional” children, members of their class, and (2) the excluding, suspending, expelling, reassigning and transferring of “exceptional” children from regular public school classes without affording them due process of law.

The cases continued to increase, even leading to the passing of Public Law 94-142: The Education for All Handicapped Children Act of 1975 and the Individuals with Disabilities Education Improvement Act of 2004, as well as many others.
https://www.wrightslaw.com/law/art/history.spec.ed.law.htm