Q:

Minimum level of technology to have a modern tax system? 

As is my understanding (this is not my specialty), for the vast majority of history the crown (whatever sovereign entity exists at the head of the state) gathered income through a few means:

Tariffs (relatively easy to implement, but don't work for domestic goods)
Stamps (also relatively easy to implement, but hard to balance with cost of doing business across businesses)
Royal charters (this also effectively covers any centralized licensing system)
Feudal tithes (and then the sovereign entity becomes someone a little closer, but the same problems ensue)

The problems with these methods is that they have a cooling effect on growth.   Royal charters in particular prevent people from investing capital and creating businesses to fill a market need.   Feudal tithing engenders mismanagement by feudal lords.   Tariffs in a low-technology environment are easy to circumvent (hence the whole smuggler occupation).   Uniformly priced stamps make small transactions prohibitively expensive. 
The state has need of capital for various uses (defense, civil order, public works, etc.).   So it needs some taxation system.   What is the minimum level of technology necessary to implement a basic form of a modern tax system (be it VAT or income)?   How would it be circumvented?   How would it be enforced? 
Edit:  I should be clear that I'm trying to avoid taxation schemes that will obviously lead to mismanagement /undue pain on the populace.   Things like selling of tax collection licenses encourages legbreakers. 
Its obviously true that any tax is going to have a cooling effect on growth (Assuming that tax money isn't being spent on public good).   But some tax systems are worse about this than others.    Let's consider an optimal tax as that which causes the least pain in the populace per unit revenue.  

A:

It's not technology which makes an income tax possible, but the political system.   In order to collect a fair, broad-based income tax, you need an accepted rule of law.   (I say "fair" and "broad-based" because confiscation is always workable, and even an ancient society could tax based on looking at a rich person's wealth-producing properties and assessing them a fraction of what they ought to be able to produce.   This is not workable on a mass basis nor is it workable if it is to be based on actual income.) 
You need a rule of law because a fair and broad-based income tax depends on being able to know what peoples' income has been.   This implies considerable organization and basic societal cooperation.   It also requires that honest accounting is the norm.   (If accounting is basically meaningless, it will quickly devolve into confiscation.) 
(The same would be true of a VAT.) 
The technology needed is little more than good record-keeping and basic accounting.   The Romans had the former and the latter was an early Renaissance innovation which the Romans could certainly have developed. 
Addendum: It occurs to me that medieval Europe had a rough and ready income tax in some  areas where farmers paid the local baron and the local church (which between them was most of the government they ever saw -- police, welfare dept, hall of records) a percentage of their crops each year.   That's an income tax by any definition.   (In other areas they paid a fixed amount, making it more like a poll tax.)   Note that no accounting was needed, since the amount of the harvest each year was visible to all. 

A:

I have a different slant than the two previous answers, but only slightly:

First, you need a money-based economy, or at least one which routinely puts monetary value on things.  If the land owner gets "one fat hog on pentecost" from each tenant farmer, the state doesn't want a percentage of those hogs, it wants money. 
Second, you need a high division of labor.  If the average household does much of their own food production (kitchen gardens), clothes production (spinning wheels and looms), etc.  then it is hard to tax a fraction of the income or value added. 
Third, you need widespread literacy and numeracy to record the transactions from the first two steps. 

One possible workaround is mandatory division of labor with taxation at this step.  Say the farmers are not allowed to mill their own grain, they must go to the overlords' windmill that will keep a fixed percentage.  The possession of hand mills is a crime.  Still rather close to the feudal tithes concept, of course.  So you cannot really avoid a society where people handle cash on a daily basis. 

A:

For effective collection of VAT the recent states had introduced special counters (I am not sure about the name), that every or every medium or big seller should have and use.  All this automation was introduced during the last 10-20 years.  So, even 20 year old technology cannot fully support the contemporary tax system.  
But that is correct for the contemporary society only. 
I agree that the technology is less important than the political system, but even more important is the moral level of the society.  In the more honest society you can use much more complicated tax system without the need of any complicated control.  
Another very important parameter is the size of the society.  In the small town-state everyone simply sees into the pocket of everyone else.  And you can easily make any intelligent tax system to work without any technology.