Are you thinking of stringers on the outside or the inside? They would have to be stuck on the fibreglass or so shaped that the fibreglass will conform, but that will create hassles when you fibreglass. On the inside you might have to watch that they don't get in the way of the seat and you would have to watch your foot placement and any steering as well.
I don't think that the stringers would stop kinking much except on the inside. I had a fibreglass kayak once and I reinforced it with fibreglass over a 1 inch hose I used as mold down the centre on the inside. That did help stiffen it but that kayak had a suspended seat. Otherwise it might have been a little rough. :-)
If I had to do that again I would make sure that around the cockpit area of the deck was strengthened as that is the weak spot in the backbone of the kayak and any kinking must occur there and that is where the weight usually is centred.
JohnK

: Not a bad idea John. What about putting in place stringers at a few points
: along the hull to give additional stiffness? I'd do this after glassing
: the inside, then laying tape over the stringers.

: Would this be a good compromise?

: I do plan to mainly us it in bays/lakes/rivers but may encounter swells, not
: much chance I'll be launching/landing it in heavy surf.

: Regards,
: Darren