As an L-2 spouse he is employment-authorized incident to status, so working from the United States is permitted from an immigration perspective. Whether he can serve Canadian clients from a US address raises tax, licensing and professional-registration questions that are separate from immigration.
Immigration permission is only the first question
The L-2 spouse's work permission is broad: it does not restrict him to a particular employer or field, so a self-employed bookkeeping practice is allowed from the immigration side. He should be prepared to show a prospective client or bank how that authorization is evidenced. The remaining questions are not immigration questions.
Serving Canadian clients while resident in the United States affects his personal tax residency, may require US state business registration, and could involve professional body rules if he holds a designation. Health coverage, banking and the treatment of Canadian-source income should be reviewed with an accountant. For the household, the important point is that the L-2 spouse's position is much better than a TD spouse's, which is one reason the L-1B route, if the specialized knowledge is genuine, may suit a two-income family better than TN.
Children under 21 receive L-2 status but cannot work.