If tax codes are simplified, how will that change the professions/jobs in the tax/accounting world?

It would depend on how much the tax codes are simplified and where. Both individuals and corporations are subject to numerous different level of taxation on the federal, state, and sometime local level.

If there was significant simplification, for example to federal individual taxation, it could reduce the need for tax assistance. Still, most people prefer to file electronically and would want to put together the tax forms themselves; so there would still be business for individual tax preparation companies like H&R Block and Turbo Tax. It could reduce the need for, or a least the number of hours, for professionals working on complex individual tax returns.

In the corporate world, tax accountants don't just work through the complex rules of the tax code, but need to gather together the information needed to prepared the tax return from the accounting records. Tax has their own accounting rules which make adjusting accounting records to a tax basis necessary. Even if the tax code was greatly simplified there would still be a need for tax accountants in large organizations (either hired by the company themselves or by hiring an accounting firm to provide the services).

Generally, it is unlikely that the tax code will ever be simplified to such a degree that the services of a professional will no longer be required. It could reduce the overall demand for these services but they will still exist.

I think it's safe to say that simplifying tax codes would result in a larger number of people doing their own taxes and fewer folks being hired by them to do this. But there's another aspect. Tax codes are put in place to manipulate the taxpayers into particular fiscal behaviors that politicians think will benefit society. There are those that also think these are to benefit certain parts of society or at least particular groups or industries. But they are intended to have an effect. Simple examples are tax credits for children, for home ownership, for certain business activities, for charitable contributions. It would be very hard to make a blanket statement about how "simplification" will effect these, because we don't yet know what counts as "simplification".

My own feeling is that any simplification will be strongly resisted because it will deprive someone, somewhere of a method of controlling, or at least influencing, society. And whether that influence is good or bad is obviously up to interpretation. Most would agree that encouraging charitable giving is a good thing. Some tax "loopholes" are good for the beneficiaries and bad for others. And some think that whatever their particular tax regulation they favor is simply in the cause of societal good.

The bottom line is that the first effect -- reducing the number of tax preparers -- is fairly obvious. And the second effect is subject to quite a lot of variables.

While some aspect of tax codes are simplified, there are also a lot other items are happening, such as GILTI (Global Intangible Low Tax Income), BEAT (Base Erosion and Anti Abuse Tax) and other international taxes.