In PostgreSQL with JSONB you can use the containment check:
dict = {"telephones": [{"telephone": "54435345"}]}
user = cls.query.filter(your_table.contact_info.contains(dict)).first()
In MySQL it might be possible to use func.json_contains:
from sqlalchemy import func
# JSON_CONTAINS returns 0 or 1, not found or found. Not sure if MySQL
# likes integer values in WHERE, added == 1 just to be safe
session.query(Story).filter(func.json_contains(Story.section_ids, X) == 1).all()
(you need to adapt and try it out, certainly the MySQL way, but probably also the PostgreSQL one)