You indicate the clothes smell like they are burning, but you did not indicate that they are overly hot. You could be smelling lint that has caught fire under the dryer drum. Since your dryer is gas it can happen if there is an accumulation of lint on the base of the dryer. You did not indicate if youâ€™re using Natural gas or LP gas. The burner flame could also be too high too.
If your doing any painting, varnishing or using any type of chemical that is used to prep wood or used in paint, the fumes will mix with the open flame of the dryer burner and cause a strange chemical type odor too.
I recommend removing the toe panel below the dryer door and inspect and clean the base of lint. I added two (2) images of the toe panel. Key#46 is the retainer clip securing the toe panel to the cabinet and door panel. Use a putty knife and insert it as shown in the first image. Push the clips down to release and hinge the top of the toe panel towards you and lift it up and off.
Once the toe panel has been removed, start the dryer and watch the burner ignite. The flame should be drawing back into the burner funnel, but not all the way up into the duct assembly (key5 in last image).
If the clothes are getting excessively hot, it may have a bad operating thermostat.
I recommend calling a service technician for safety concerns to diagnose and repair your dryer.