Are flame tests useful in determining identities of metals in a mixture of two or more salts? Why or why not?
Yes and no. A flame test will only really show the brighter or more visible flame of a given metal ion when one or more metal ions are present.
For example, Sodium burns with a strong orange flame whereas potassium burns with a delicate lilac based flame. If you have a mixture that contains both of these ions, the likelihood is that you would only really observe the stronger orange flame and thus would be able to conclude that sodium is present in the mixture but not be able to identify the potassium.
Therefore it is useful in a limited capacity.