One marketing principle that comes to mind is to figure out who else already has your ideal customers -- in this case, local union members (i.e., typically, blue-collar workers of various types) -- as customers/clients or members. Where do they hang out? What else might they have in common? In other words, affinity groups.
As Pete said, the Union Hall / meeting place itself would be a natural fit, and an endorsement from the union would be terrific, but I don't know how realistic that is or difficult to work with they may be. (Never having belonged to a union, nor talked about it with friends who do/did, I can't really say.)
How about the local watering holes, where they go for drinks afterward? Or, the bowling alleys? Or, sporting goods stores? Or,... well, you get the idea. I'm not too sure if flyers is the way to go, but they ought to get a better response from these places than in the newspaper. (Personally, I rarely look at those flyers, and never for professional services.)
Consider endorsements, cross-promotions, and other forms of joint venturing. Consider sponsorship of sports clubs (little league?) and/or holidays (Secretaries' Day?) or other events. This can lead to free publicity if handled right...
The local ValPak or Super-Coups might work well, especially if the ad is well-designed (from a marketing perspective, that is). Concentrate on benefits and make an attractive offer (not some measly 10% off thing).
Ideally, your Doctor client should have a Unique Selling Proposition (aka Distinct Buying Advantage, from the prospect/customer's perspective) that makes their ideal prospect see her/him as the ONLY one worth going to. Perhaps, if s/he can simply (& honestly) say that they specialize in the injuries & illnesses typically suffered by union members (e.g., back strain, carpal tunnel syndrome, hernias, etc.) and in dealing with all the relevant insurance plans, your marketing strategy should be organized around that. Even if your client is not the only one who handles that stuff, if s/he is the first to say/emphasize it, the strategy of "pre-eminence" can work to make her/him the one who is known for it.
My final thought on this (for now, at least) is that the Doctor should offer some sort of free informational product as a way to get people's contact info. It must be something relevant to their needs/wants and not readily available (at least, not for free). For example, "Top 10 Ways to Avoid Back Pain" or "Six Dirty Secrets Your Insurance Carrier Doesn't Want You To Know". Several booklets/tip-sheets addressing different injuries/conditions would be great for targeting different industries. They could be offered via newspaper ad, YP ad, ValPak, radio ad, etc., as long as the prospect is required to give you their contact info (e.g., via snail mail or voice-mail). The second step is, of course, to include more information w/ the requested booklet(s), perhaps in the form of a brief, charming letter with an offer they can't refuse. 8^]