How can I get my child tested for dyslexia without going through the school system?

The least expensive. way is to utilize a graduate program, since insurances rarely pay, Contact CHOP; or your International Dyslexia Association branch, Read "Overcoming Dyslexia" by Dr. Sally Shaywitz. 90% of cases are language-based, caused by lack of phonological awareness. "Vision training" & " Brain Balance" are unproven therapies.
Pay privately. There are lots of reputable psychologists, neuropsychologists, and educational psychologists who do this kind of testing, along with intervention programs such as lindamood bell and slingerland. Probably can arise, though, if you want services through the school and the school does not accept the findings of an outside tester. It really depends on your concerns and goals.
LD assessment. Assessment of dyslexia if done properly will assess general abilities, processing difficulties that may contribute to the dyslexia and evaluate for other learning disorders or conditions which could lead to school difficulties. For detailed discussion see: http://ldassessment.Com unfortunately in these days of budget cuts, school systems are using a system of trial and error before testing.