Linear economy models are no longer acceptable for the plastic industry and a change to a sustainable circular plastic economy must take place. In the field of thermoplastic foams, the biopolymer poly(lactic acid) (PLA) is a suitable alternative for fossil based foams like polystyrene. However, the production of PLA bead foams is still a challenge. In regards to circular plastic economy products, a reduction of the needed polymer additives is aspired to simplify the union of end-of-life plastic streams. Flame retardants (FR) are required in many applications and are often the largest proportion of additives. It turns out that the removal of FRs, for example the removal of the REACh registered FR hexabromocyclododecane for polystyrene foams, requires a great effort. This paper shows that PLA bead foams require no FR to achieve a class E classification for construction products. Therefore, nine PLA types are analyzed by differential scanning calorimetry, thermogravimetric analysis, gel permeation chromatography, and rheotens measurements. From five types, PLA bead foams could be produced with two different densities. In addition, PLA bead foams containing 1.5 wt% alkoxy amine FR were produced. The flammability of the PLA bead foams was investigated by LOI, DIN-4102-1-B2, and cone calorimeter tests.