The flight safety regulator says Amazon shipped the packages without warning labels, paperwork that specified the chemicals inside, or emergency response information.
The proposed penalty comes two weeks after the FAA fined Amazon $350,000 over a similar incident that caused injuries to several UPS workers.
The first of the two latest fines relates to a shipment made in May 2014, when Amazon sent two packages containing a rust-stain removing product from Illinois to Florida. One box contained four 1-gallon plastic jugs and another two jugs of the corrosive chemical.
The shipments were discovered by FedEx workers when they began to leak.
The second shipment was in June 2014, when Amazon offered UPS a box containing a 19-ounce container of Simple Air EZ Green HVAC Cleaner. The flammable gas was discovered by UPS workers in Kentucky.
Two weeks ago, Amazon was fined for sending a gallon of Amazing Liquid Fire, a corrosive drain cleaner, by air from Kentucky to Colorado, in October 2014. On that occasion, the container leaked and nine UPS workers had to be treated for a burning sensation on their skin.
Amazon has 30 days to respond to the allegations.
The company did not respond to a request for comment Wednesday, but in response to the fine two weeks ago it said: "We ship tens of millions of products every day and have developed sophisticated technologies to detect potential shipping hazards and use any defects as an opportunity for continuous improvement."