You have Solaris 10 media but which revision? Is it an older version which uses "boot archive"? (That's prior to 10u3).
There are two ways to update firmware; from the system processor SC> prompt without Solaris running, or from Solaris # prompt with Solaris running. Booting into single user means that Solaris is running.
One really handy utility is "sysfwdownload" introduced in latter years (Google that). That is a Solaris utility that will download the new firmware file directly inot the Service Processor and "park" it there in reserved space. When you reboot the SC it notices the new file and asks whether you want it flashed in. If you say yes, everything is done for you.
With the SC only method you can download the new firmware from a tftp server. Do you have one of those or can you quickly build one?
Reading your post and the specific error message that you posted, take a look at this link near the bottom. If the Solaris 10 is prior 10u3 there's other steps needed.
Upgrading OBP and ALOM on a SunFire v210/v240 « Weblog for Thomas S. Iversen
Good luck. Let us all know how you get on. Continue to post your questions.
---------- Post updated at 12:46 PM ---------- Previous update was at 12:12 PM ----------
And also..............
When you talk about the file "flash-update-SunFire880-latest" where did you get that? I seem to remember that when you download (from the internet) a firmware upgrade it comes in zip form and you need to unpack it and then set permissions on the file(s) to 755. I think that often there is more than one file unpacked from the zip and you need to set any/all to 755.
Can anybody confirm that please?