One reason that your FlexReport daily total may not align exactly with the Cost History report per day total is due to apportioning.
Apportioning takes place in the Cost History report and allows you to view the recurring cost (different from the upfront cost) of all your RIs included in the hourly fee calculation for each usage line item in the AWS bill. This is particularly useful for chargebacks and showbacks.
The FlexReport data is derived directly from your CUR line items, where apportioning is not applied.
You can compare the sum total of all the per-day spend to ensure that the overall totals between two sources (FlexReport and Cost History) align.