We moved - genuinely moved - into a tiny rented house near to a good school when applying for an in-year place for DS and a [late applicant] Reception place for DD.
HOWEVER, our 'owned' home was 35 miles away, in a different county, and although not sold at that point, could easily be identified as having been on the market for [grrrr in retrospect] ages.
We were also clearly in the process of genuinely moving to the area - transferring doctors, etc etc etc.
We didn't encounter problems, though of course we had to supply reams of additional paperwork in connection with the applications - rental contral, council tax bills, evidence that iur house was for sale, etc etc.
If you sell your house, an move into a rented property near your chosen school, you MIGHT be OK - it would obviously depend on whether the flat was genuinely big enough for you, and whether the LA is one of those that investigates 'potentially fraudulent' applications with vigour.
In some LAs, address at the time of school entry is checked against address at time of application, and any address moved from in the months before application, and if all but the rental address are outside catchment for the school, then the child's place is revoked (especially in the egregious cases whether the family is moving back into the property that they have owned all along).
So I would say that in many LAs, you are already too late to move without falling under scrutiny, and if you do move it should be after sale of your current house. You should look to stay in the flat for up to a year AFTER your child starts school unless moving to a new house still within the catchment area.