I have a 2005 Dodge Durango and the oil light flashes but only when I'm stopped. Oil was changed last month and filter as well.
If you have already verified that the oil level is correct (check the dipstick, read your owner's manual if you're not sure), it looks like this vintage Durango has a known issue with the oil sending unit. Source: Google Call a trusted mechanic or dealership and ask them about this. If you have a suggestion of the issue, they'll hopefully be less likely to fleece you on that repair costs!
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