I am using Gentoo Linux and I have no problems with flash. There is a bug report with a workaround for this on the Fedora bug tracker. It is not an Nvidia problem:
The issue is that flash uses memcpy() where it should be using memmove(). The change in glibc to memcpy() broke the incorrect code and Adobe so far refuses to fix their bug. The workarounds that can be done are to patch the binary to call memmove(), patch glibc to only copy forward or downgrade glibc.