My son is in Kindergarten and he has had 2 BM accidents at school. He is an only child and I'm afraid that at home with our constant reminders, he has never learned to go for himself. How do I in essence potty train him? I do not know how to carry through with a natural consequence (which I guess is let him soil himself and take care of it) due to the situation. I cannot think of a logical consequence that is relevant.
The problem you describe while embarrassing for your son and upsetting for you is not altogether rare. At this stage of a child's development there can be multiple reasons for what your son is experiencing. You don't mention how old your son is or when your son began consistently using the bathroom. But while the average girl is potty trained by 35 months and the average boy by 39 month, there can still be "accidents" in some children until age 7.
There can be a number of possible reasons and solutions for the situation your family is experiencing. The simplest and most common interpretation is that his new school is just too interesting for him to bother being interrupted from his focused concentration of all the fun and interesting things happening around him to remember to stop and use bathroom. If the teachers are willing to remind him during the day, in a casual and definitive way that it's time to use the bathroom, this might prove helpful in breaking his concentration long enough for him to take care of business until he establishes his own new routine of using the bathroom at school.
For many children, often the change of their routine which is brought on by a new situation (i.e. school) can lead to some increased levels of stress. Depending on how your child deals with stressors in his life, he might be exhibiting regressive behavior, that is, going back to an earlier stage of development (soiling his pants) until he feels comfortable with his ability to manage the new situation, at which time he will regain his ability to have complete control over his bowels and his daily situation. Try and check how he seems to be handling this big transition to school and gauge his coping ability to get a sense of his stress level (he may not yet be ready for kindergarten, especially if he is young, he may benefit from being held back). He may just need some time to adjust and some skills to help deal with the change.
In some extreme cases (i.e. if the soiling pattern is consistently being encountered in other areas) it could be a signal of a medical problem, in which case you should seek guidance from your pediatrician.
Finally, since he is one with control/responsibility over his body the problem's solution is ultimately with him. And if it is not a problem for him, no matter what anyone else does to assist him, it will not make an impact enough for him to change his behavior. You are correct that while it is difficult for you to let him experience the embarrassment of soiling at school, he can take responsibility for the natural consequences by bringing a change of clothes to school and rising out his soiled pants and sticking them in a plastic bag to bring home. Show him in a calm and casual way how this cleaning is done. He needs to rise the soiled pants in the toilet so the contents can be flushed, then brought to the sink to be rinsed and put, wrung out, in the plastic bag and tied. Then he must thoroughly wash his own hands. This is not, in any way, a punishment - it's what needs to be done with soiled pants and you can let him know (after teaching him the skills) that this is just what one does when you have an accident. No guilt, no pressure. Often children feel somewhat relieved to know there is something they, themselves, can do when this happens. And in many cases, just being around other children who use the bathroom and don't soil their pants teaches a child that that behavior is the norm. So, as long as you have checked out some of these adult solutions/options and are comfortable that it's not a medical issue and that you've done all you can, it really is up to him from there.