Do certificates need to be stored as encrypted? The titles says most of what we're confused with. Here's some details:
On an embedded device, we have a microcontroller and external flash memory.  This memory can be easily read and written to in place.  On that memory we store SSL certificates and a private key.
The microcontrollers internal flash memory is secure and can be used to hold fixed encryption keys, even uniquely generated so are only ever known inside the microcontroller.  I cannot store certificates on the internal flash memory.
It seems obvious that the private key should be stored as encrypted but I am not so clear about the certificates.
What is not so obvious is if the certificates used to verify a TLS connection should be stored as encrypted to.  It is likely that the root level certificates will be self signed and have no chain back to a verified root CA.
Thoughts?
What is not so obvious is if the certificates used to verify a TLS connection should be stored as encrypted to. It is likely that the root level certificates will be self signed and have no chain back to a verified root CA.

As DannyNiu stated, there is no issue if someone were able to read the certificates; those are public information, and allowing an adversary to read them is not an issue.
However, there is a potential concern - what if an adversary can overwrite them?  After all, an adversary who can do that could insert his own root certificate, and then establish a TLS connection (based on the root certificate he picked).  This may or may not be a concern for you (can the adversary modify the flash, and then perform a negotiation?); if it is, one approach to prevent this would be to integrity check the certificate.  That is, you would pick a random key, and put that into the internal flash memory; you would use that key to compute a MAC of your certificate; that generates a moderate sized (perhaps 32 byte) string, and write that string alongside the certificate in your external flash.  Then, when it comes time to use the certificate, you would again compute the MAC of that on-flash certificate using the key, and check to see if the 32 byte string you computed was the same as the string that's stored in memory.
An attacker who tries to replace the certificate with his own is unable to compute the 32 byte string (because that depends on the key you have in secure storage); hence any attempt at modification will be detected.