The first thing I need to know if this is an electric or gas dryer. An electric dryer will have a big plug on it. A gas dryer will have a simple 110 plug on it.

I'm assuming an electric dryer. I'd check to make sure it has a four pin plug and that the frame is not bonded to the neutral where the cord attaches to the dryer. They come shipped so they can be installed either way (three wire hookup is legal in older houses).

Next simple test is to remove the lighbulb inside your dryer and see if that stops the problem.

I'd check carefully the neutrals from both the arc fault in question and the dryer circuit to make sure they are properly terminated (both the load side and the pigtail from the AFCI breaker). If there is any place where the neutrals could possibly touch after the AFCI, it will cause tripping (an AFCI also provides some ground fault protection though at a higher current rating than a GFCI would).