In IPv4, fragmentation is done by routers on way to the destination if DF(do not fragment) flag is not set in the IP packet.
Once a packet is fragmented, its fragments may take different paths (due to various reasons like topology changes) to the destination.
If, on some link again in the path to destination, one routers find that the link MTU is smaller than the frame size, then either the packet needs to be fragmented or dropped.
Can fragments of a packet be refragmented again? If yes, what will be the value of MF flag in the new individual fragments created by this?
Yes, they can be refragmented. Every refragment but the last will have the MF flag set. The last fragment will have the same MF flag as the original fragment. So it's just as if they had originally been fragmented that way.