My 1998 Olds 88 has been stalling and running rough.

Check what's called the map sensor. Advanced auto parts can help with that.

flashing light most always means missfire.
could even be crossed wires.to the plugs.
you really need a code reader and find the trouble code .
but in the mean time make sure the firing order is correct.
good luck .gary

Have you checked for spark to the plugs and fuel pressure ?

Do a compression test.

FUEL PUMP.
Have you checked the fuel flow and pressure?
If the fuel pump is over 160,000kms/100,000miles it's done.
Put in a complete assembly,if your mileage is close to above numbers you need a new pump anyway and it may (90% chance) will cure your rough running engine.The other 10 % is contaminated fuel and electrical, but as you have no codes I'll say FUEL PUMP.

HEAD GASKET GONE

check fuel pressure regulator.+ vacuum lines going to it look see if gas in vacuum line.if so regulator rupture.

check the mass air flow sensor in the air breather,it may have fuzz from the air filter on it

when you say stalls, do you mean shut off of just get low on power?

my check engine light comes on and then oil press light come on and the car shuts off but the lights and music stayed on.
if its that the car needs oil and shuts down to protect itself but it will turn on minutes later.

if stalls periodically, shows check engine light and the car looses a bit of power, in the engine, :

1. your coolant may be having problems getting to the engine in the way it was met to get to the engine

2. the belt might be a bit off and that could be why you get the slipping feeling

3. your exhaust may be a bit clogged. or your engine may need cleaning

i had both problems my car shut off and my engine was slipping. my EXPENSIVE but great machanic found out it was my oil level and my coolant was rusty and not getting to the engine. now she drives like the original 97 olds 88