I think you are (understandably) mixing up two related structures.
Estar acostumbrado (a) is a regular estar + adjective predicate that can take an object (introduced by the preposition a). It means "to be used (to)". Of course acostumbrado is the passive participle of acostumbrar, but it functions as an adjective.
Acostumbrarse (a) is a pronominal verb, that is, a verb that takes a reflexive pronoun (and that is customarily cited with se) even though it's not really or strictly reflexive. It means "to get used (to)".
The difference, as you see, is of state vs. process. The state is expressed using estar plus an adjective, while the process is expressed by a verb (in this case a pronominal verb).
If you want to show an ongoing process of getting used to something, you use the Spanish equivalent of the English present continuous, i.e. estar plus the gerund of the main verb, which being pronominal will carry its reflexive pronoun with it: estar acostumbrándose (a) "to be getting used (to)".
- Estoy acostumbrado. = "I'm used (to it)." (present, state)
- Me acostumbré. = "I got used (to it)." (preterite, past process)
- Me estoy acostumbrando ~ Estoy acostumbrándome. = "I'm getting used (to it)." (present, ongoing process)
Note how in the last sentence the reflexive pronoun can go before the auxiliary or attached to the end of the gerund.