Could clever logic be used so that the user is asked for raw at only one place in the code?
Yes, but this is usually a bad idea. Top-driven loops (like this one) are best. Twisting the logic just to avoid an extra user prompt is a poor trade-off.
The flowchart as it is needs a few more details.
In particular, recall that the raw scores are expected to be in the range 0 to 300. Negative values will halt the program, but it would be nice to check that positive values are in range and to write an error message if not.
Mentally, add a structure that checks that values are in range.
Also, add a few boxes to show how the entry count is handled.