Aflatoxin does not grow. The mould (eg Aspergillus Flavus) grows and may produce the toxin. Both mould growth and toxin production are dependent on mainly temperature and moisture (water activity).
There are many papers describing the boundaries for mould growth and toxin producion. One example being the Mycotoxin Blue Book. D. Diaz Editor. Nottingham University Press 2005
Aspergillus species and Penicillium species are typical storage fungi that grow under unsuitable storage conditions. Aflatoxin are some of the most important mycotoxins formed by these moulds. But also be aware of Ochratoxins. These are formed during storage if moisture and emperature are both higher than recommended. This depends somehow on the crop and the storage facilies.
There are two groups of fungi; field fungi and storage fungi. Field fungi are commonly present in the freshly harvested grain. They invade the grains before harvest or after cutting and swathing but before threshing. Storage fungi (Aspergillus spp. and Pencillium spp.) will develop on the grain if the storage conditions are poor. High moisture and temperature conditions will accelerate their growth, resulting in an increase in aflatoxin production.
As other have explained, aflatoxin is the toxin produced by certain moulds such as Aspergillus and some Penicillium spp. under the right (for the mould) conditions of temperature and water activity. The links below should help: