The pathways of BMAA (and the related 2,4-DAB) biosynthesis in cyanobacteria are not known. A recent review by Peter Nunn and Geoffrey Codd considers possible metabolic routes, by analogy with reactions used in other species, by which these amino acids might be biosynthesised by cyanobacteria, which are a widespread potential environmental source of these neurotoxins.
Reference: Nunn, P. B. and Codd, G. A. (2017). “Metabolic solutions to the biosynthesis of some diaminomonocarboxylic acids in nature: Formation in cyanobacteria of the neurotoxins 3-N-methyl-2,3-diaminopropanoic acid (BMAA) and 2,4-diaminobutanoic acid (2,4-DAB)”. Phytochemistry 144, 253-270.