It depends upon the specific fare. Many United flexible fares are published and have no sales restrictions, so a travel agent should be able to book them. Some are unpublished / web-only fares that can only be purchased via United. Generally, if you see a fixed, round-number buy-up between regular economy and flexible across a large set of flights -- and if they're booking into the same fare bucket -- those are probably using the unpublished fares.

Rather than quoting a fare basis, it may be best to say "I want a fully refundable fare" or "I want a fare with no change fees" or whatever is important to you. Then, compare the price they offer you with what you saw online and that can give you a pretty good idea whether or not you're getting what you expect.

Definitely do not say, e.g., "I want an H fare" or something like that, based upon seeing an H fare in the flexible column on United.com; United may publish many fares in the same class, and some can be non-refundable while others are fully changeable and refundable -- even on the same route and the same dates.