Is iterative sha256 adequate for local password manager?
I will skip the usual don't roll your own speech. 
For a local password manager you typically need encryption   not only password based key derivation.
You want to encrypt your various passwords with a key derived from your master password.
There are many methods for doing so, argon2 is one of the best. However iteratively applying a general purpose hash function is also acceptable. An example of how to use a general purpose hash function is: https://en.m.wikipedia.org/wiki/PBKDF2 

Note it mixes the password again in it's iteration and xors the results these ensure the space of possible outcomes doesn't shrink with iteration count as it would with naive chaining. Also note the use of a Salt which prevents attacking multiple passwords together or use precomputed dictionaries/rainbow tables.

Argon2 is also memory hard and argon2i is also side channel resistant not sure these are a must.

With such a key derived from your master password you can encrypt the individual passwords with a symmetric cipher of your choice. 

Note there are other things to watch out for when building your own password manager. For instance, be sure to ask lock the sensitive memory to never be swapped to disk. Or your master password and key may find themselves on disk  so that anyone can read them.