The school aren't likely to agree to flexischooling, for the reasons mentioned by @viques and @bestsellingshow . It is at the head's discretion whether to allow it, except in cases such as the child being below "Compulsory School Age" or having an EHCP specifying flexischooling. You could ask, but I wouldn't be optimistic.
However, I think your daughter would make great progress with one-to-one attention from you or tutors. It is vastly more efficient than mass instruction. (I don't get the impression that @Singleandproud has any experience of home education, as their concerns about it are really quite misguided, especially since you are only planning to pursue this arrangement for six months or so.) It can be hard to cram extra learning into school holidays, weekends, and after school (a model sometimes called "afterschooling") because the child is often too tired and turned off learning from having spent so much time at school.
You might consider pulling your daughter out of school altogether to home educate. Y6 is a great time to do it, since you don't have to worry about whether there will be a school place for her at her old school, and she can just join Y7 alongside all the other new starters at secondary next year.
Besides, some schools waste much of Y6 "teaching to the test" for SATs. I know some parents who have home educated for that year only, purely because their kids were made miserable at school with endless mock SATs rather than real learning. Depending how your daughter's school approaches SATs, she might not miss much if she is out of school this year.
That leaves you with the problem of childcare for the three days when both parents work. Could you afford a childminder? If you are on a low income and receiving benefits, you can get some help toward the costs. I used to work part time, and sent my child to a childminder who was also a home educating her own kids. My child played, read books, and went on social and educational outings with the CM and her kids. It was a great arrangement for us.