i don't know which device exactly you're referring to as there is no "HP Pavilion 14 Chromebook", but there is the older "HP Pavilion Chromebook" and the newer "HP Chromebook 14". the former didn't support legacy boot so you'd need a custom firmware to boot Ubuntu directly w/out building the kernel specially, but the latter includes legacy mode (CTRL+L) so no firmware modification should be necessary. you will need to know the exact model though in order to download the correct recovery/firmware image.
that said, i don't know exactly the process you went through, but the SPI flash includes multiple sections -- the firmware itself, as well per-device factory settings (like serial #), so hopefully that wasn't blown away :).
every CrOS recovery image actually includes the firmware so you could extract it from that. this file:
https://dl.google.com/dl/edgedl/chromeos/recovery/recovery.conf
indexes the latest recovery image for each board. fetch the right one, then unzip it, then do:
losetup -P /dev/loop0 <bin file>
then mount the rootfs:
mount -o ro /dev/loop0p3 /mnt/somewhere
then you have the firmware script:
/mnt/somewhere/usr/sbin/chromeos-firmwareupdate
you can get the files themselves by using the --sb_extract flag, but the bios.bin in there is the full flash image and won't include the factory data. so you will have to manage extracting the specific coreboot payload/whatever and writing it to your flash. you might be able to get away with running that script directly with --mode recovery ... not entirely sure. but you can pop open the script itself to see what the different modes do.