The 6809 and 6809E are software compatible. Some later CoCo3's had the Hitachi 6309 which has extra instructions.
If the CoCo3 has a normal 6809 and is running OS/9 or variants thereof then I would expect some software compatibility. Not sure about Flex as the Video memory overlaps the flex memory space, but I think there were some patches (hardware & software) to allow things to work...
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