The short answer is no. The long answer is yes.
Acrylic paints, by their nature are not flammable. What is flammable is the vehicle used to emulsify and carry the pigments so that they are evenly distributed in a liquid.
Acrylic house paint is usually not flammable because the vehicle is generally water or another inert vehicle. Most craft paints also fall into this group. Model paints, depending on the maker, can use alcohol and other esters as part of the vehicle. These alcohols generally act to cut the drying time.
One last consideration... if you are spraying paint, you can accululate enough of a particle cloud to promote explosion. Again, the paint itself may not be flammable, but the cloud gives the sparks enough matter to convert to energy.
So, to answer yoru question... yes and no. Read the label and act on the safe side.