You will need to mount the root partition of your new install to a filesystem in your flashdrive linux's /mnt/ and chroot to it.
example..
lets say your new install root part is /dev/sda1
and you are root
Code:
mkdir /mnt/sda1 ; mount /dev/sda1 /mnt/sda1
mount --bind /dev /mnt/sda1/dev
mount --bind /proc /mnt/sda1/proc
mount --bind /sys /mnt/sda1/sys
chroot /mnt/sda1
grub-mk-config -o /boot/grub/grub.cfg
grub-install /dev/sda
exit
cd ~
umount /dev/sda1
Shutdown, remove flash drive and reboot as normal.
In your BIOS, doublecheck your boot order and prior to that use fdisk or gparted to verify your new install partition has the boot flag enabled.