A flashing Check Engine light means that 'whatever' the cause is, its damaging Emissions components.
In most cases, the engine is Misfiring.
Best way to find out is go to a parts store (Autozone, Checker, Napa, ect..) They should have a Code Reader in which you may borrow to read the codes for the Check Engine Light.
That will read the code/codes in a P_____ (Dashes will be numbers) and possibly tell you what the code translates too. If it doesn't you may have to use Google.com, type it in for the car and read up on what the code is.
Then act upon repiar.
The dashboard dude
The 2014 Dodge Avenger has an inline 4 engine.
The 2011 Dodge Avenger has an inline 4 engine.
The 2012 Dodge Avenger has an inline 4 engine.
The 2010 Dodge Avenger has an inline 4 engine.
The 2008 Dodge Avenger has an inline 4 engine.
The 2009 Dodge Avenger has an inline 4 engine.
The 2013 Dodge Avenger has an inline 4 engine.
A flashing check engine light is an indication of an engine misfire.
It looks like a little yellow engine.
The 2014 Dodge Avenger has a 2.4 L base engine size.
The 2011 Dodge Avenger has a 2.4 L base engine size.