There are several things happening here, I think.
First of all, a superlative does not always have to literally refer to a singularity. Superlatives are commonly used as amplified comparatives. This can, as @Oddthinking remarks, be seen as hyperbolic use of the superlative:
We had the best time last weekend!
That doesn't mean we necessarily had a better time last weekend than we had at any other point in time. Likewise, a best friend is not necessarily a better friend than all others.
Secondly, as, others have said, best friend can be short for one of my best friends. Superlatives can be used to describe a group of items:
The three best books I have read are ...
And finally, yes, some phrases suffer semantic deflation. Even assuming that best friend can refer to one of several people, the expression best friend forever (BFF) has been in use for a while in on-line media. Interestingly, people report that they have "a new BFF", which seems contradictory to the strict semantic interpretation of the expression. It seems people use the expression rather as "a person who they see as quite a good friend at this moment", rather than "the person who will for all eternity be my one best friend". Ah, well, language is the darnedest thing!