As for Blender 3.6 the script by @iyad-ahmed stopped working because Blender added new builtin orientation PARENT.

Previous script was relying that there will be exactly 6 builtins, I've updated the script so that it will get the actual list of builtin transformations so it won't break the next time Blender adds/removes new transformation.

PS there is still no other way to get list of all custom orientations besides parsing exception message and excluding builting.

import bpy

context = bpy.context
transform_slots = context.scene.transform_orientation_slots
builtin_transforms = [i.identifier for i in bpy.types.TransformOrientationSlot.bl_rna.properties['type'].enum_items]

# hacky (but the only way) to get the all available transforms
try:
    context.scene.transform_orientation_slots[0].type = ""
except Exception as inst:
    exec("transforms = " + str(inst).split("in")[1])

for transform in transforms:
    if transform in builtin_transforms:
        continue
    transform_slots[0].type = transform
    bpy.ops.transform.delete_orientation()

As for Blender 3.6 the script by @iyad-ahmed stopped working because Blender added new builtin orientation PARENT.

Previous script was relying that there will be exactly 6 builtins, I've updated the script so that it will get the actual list of builtin transformations so it won't break the next time Blender adds/removes new transformation.

PS there is still no other way to get list of all custom orientations besides parsing exception message and excluding builting.

import bpy

context = bpy.context
transform_slots = context.scene.transform_orientation_slots
builtin_transforms = [i.identifier for i in bpy.types.TransformOrientationSlot.bl_rna.properties['type'].enum_items]

# hacky (but the only way) to get the all available transforms
try:
    context.scene.transform_orientation_slots[0].type = ""
except Exception as inst:
    transforms = str(inst).split("'")[1::2]

for transform in transforms:
    if transform in builtin_transforms:
        continue
    transform_slots[0].type = transform
    bpy.ops.transform.delete_orientation()