As a teacher it is a different experience. I am doing a job that suits me and fits in with my life style, I'm not looking for it to provide friendship. You can sometimes miss out on things that people thought you knew but you had missed, but you tend to get passed on the important things. It is nice if it is friendly, but if it isn't I can just eat a sandwich and work through breaks. It isn't like being a pupil, I don't need to eat my lunch with someone and I don't have to go out in the playground hoping that someone will talk to me. I am doing the teaching and know what happened when I wasn't there so I'm not the one mystified by the maths because I missed Tues and Wed and Thurs makes no sense without those lessons.I'm never the one who starts a project late and finds that I am put in the group with the least number of people and they have already started practical work and I didn't have any choice because I wasn't there.
A small alternative school, set up to work in a part time way for all pupils, would work fine. I think that if you try and do it mainstream then for you to be flexible, you are wanting the rest to have a rigid timetable, which isn't fair. For example I can see that the flexi pupil may have arranged to be in on Tues mornings for maths but the class were engrossed in topic work on Monday afternoon and the teacher wants to go straight on with it on Tues morning while they are all keen, this is no problem for everyone else, they can do maths in the afternoon. However it is a problem with the flexi DC because they are going at lunch time and won't get the maths-worse than that they are not doing the topic because it isn't 'their day' and so they are 2 weeks behind, have no book, no resources and not a clue what is going on.
It could work if it is a very alternative school, e.g. one I know, that do their own timetable and as long as they are there on a Monday for input they can do it when they like-they could even carry on at home if they wanted or it would work in a very traditional school where they work to a timetable that is set in stone and so if you are going in for maths on a Tues at 9am, you know that that is what they will be doing.
It could work in reception-but gets more difficult after that.
My nephews did it for GCSE and it worked brilliantly for the lessons, they got on well with the other pupils-the problem came at break when the others met up with friends in different lessons who didn't know my nephews at all-that is where you get left high and dry unless you are a very confident DC-it is a nightmare for the shy.
I think that to go for flexi schooling is a misunderstanding of what schools are about-it isn't just the lessons. It is better to throw yourself whole heartedly into school or HE, IMO-(speaking as a once very shy DD).
Setting up a small school of your own run on flexi lines would be the best of both worlds.