Flexitime for teachers doesn't mean changing the school day for the kids!
Let's say a school has 6 periods a day, & a standard teacher allocation is 25 taught periods.
So usually, you'd get an average of 1 free period per day - in reality you might have a couple of days when you teach all 6 periods, then another couple when you have 2 frees. Whatever works for the timetable.
In theory, you could have a weekly half day off. Let's say you don't come in on Tuesday until lunchtime.
You'd be physically in school for 27 periods, so it would be very full on, with only 2 frees available across the other 4 days in order for you to satisfy the requirement to be teaching 25 periods in total.
Not many schools are necessarily going to be able to facilitate this - it would depend an awful lot on subject & which year groups you teach. But it's the same principle as teaching a 0.8 timetable, where, say, you aren't in on Tuesdays full stop, & teach 20 not 25 periods with your salary reflecting that; this is a very common arrangement especially for parents of young dc who teach.
It's reasonable to ask. I have a woman in my department who does exactly this compressed week: she is out of school one afternoon a week because of childcare issues, but still teaches a FT number of lessons over 4 1/2 days.
She would actually have been perfectly happy with 0.8, which was her original arrangement in September, but is doing a compressed week as a favour this term because we've lost another colleague & not been able to fill his post, so she's part of the solution to that.
It's worth asking, OP.