ASTM C 67 has a method to test for efflorescence, but it is meant to be conducted before the brick are shipped to the job. While it will not result in a quantitative amount of efflorescence present, it will indicate if the brick effloresces or not. Unfortunately, this test is not appropriate for brick that have already been built into a wall.
Chemical tests on existing efflorescence could be done to find the type of salt present. A masonry consultant should be contacted to make this determination.
For additional information on efflorescence, see Technical Notes 23 and 23A.