How many people were killed by Protestant Inquisition style tribunals? Asking for references/estimates

To answer the question we must first consider which countries became Protestant around the time of the Reformation. There were eight (I think): Scotland, England, (Ireland, sort of of), Switzerland (parts), the Netherlands, Germany (parts), Denmark, and Sweden.

Did any of these countries set up “Inquisition-style” tribunals, and if so, how many people lost their lives through them?

I don’t think that any of these countries set up “inquisition-style” tribunals during the sixteenth century, so the answer to the question in that sense would be zero.

If the question is broadened out to ask how many people lost their lives judicially for religion (as opposed to being killed in war, or murdered, or executed for other reasons), then obviously the answer is non-zero, Michael Servetus in Geneva being a case in point.

In England a number of Roman Catholics were put to death under Elizabeth, listed here, but also some Protestants such as John Penry.

In Scotland, there was a Roman Catholic inquisition of sorts in the fifteen century (see Laurence of Lindores), and Paul Kravar (Craw) and others were put to dead. This seems to have lapsed in the sixteenth century, and Cardinal David Beaton, although an occasional persecutor of Protestants, did not attempt anything systematic. His successor, Archbishop John Hamilton, was even less inclined to this, and the two Protestant martyrdoms during his tenure (Adam Wallace and Walter Milne) are rather puzzling.

After the Reformation of 1560, the Mass was prohibited on pain of death, but this was never inflicted (see, for example, Thomas McCrie, Life of John Knox (1855 edn.), pp. 175-6, 226). The Dominican friar John Black was murdered at the same time as David Riccio, but there were no judicial executions. There was a Roman priest executed around the 1580s, but arguably for some political misdemeanour, and then there was the famous case of John Ogilvie in 1615.

In speaking of “inquisition-style” tribunals in Scotland, the OP is probably thinking of the covenanting period of the 1670s and 1680s. There were certainly resemblances, with people being apprehended, brought directly before the supreme court which was the Privy Council (which included bishops), and tortured. But there were also differences, and one would need to think carefully before equating the two. Quakers and Romanists were imprisoned at that stage, but all the people put to death were Presbyterians. However, this was more than a century after the Scottish Reformation, and not very relevant to the question.

Edit: In answer to some of the comments below, I have checked a few works, and scholars of the European Reformation commonly deal with it under the geographical headings broadly associated with modern countries. Thus in ‘The Reformation in National Context’, ed. Bob Scribner et. al. (Cambridge University Press, 1994), the chapters are entitled: 1. Germany; 2. Switzerland; 3. France; 4. The Low Countries; 5. England; 6. Scotland; 7. Scandinavia; 8. Bohemia; 9. Hungary; 10. Poland; 11. Italy; 12. Spain. It is understood, of course, that most of these geographical ‘regions’ had very different political arrangements in the sixteenth century, but it is convenient to work with modern labels.

In eight of these divisions (Germany, Switzerland, The Low Countries, England, Scotland, Scandinavia, Bohemia, Hungary) there were sovereign entities which accepted Protestantism in the sixteenth century, and which would have to be considered in connection with the OP’s question and religious persecution. In addition to what I said above about Scotland, it would appear from the relevant chapter in Scribner (pp. 1191-21) that there was no systematic religious persecution in Lutheran Denmark.

I suspect that the phrase “Protestant inquisition style tribunals” has created a difficulty because there are no such references to be found on Wikipedia. Yes, there is lots of information on the Scottish and English Protestant Reformations, but nothing about any sort of “inquisition” against Catholics. Yes, King Henry VIII started off a terrible purge against Catholic abbeys, stripping them of all their wealth so he could swell his own coffers. And right here, where I live, is physical evidence of four abbeys that he destroyed. But “inquisitions” where individuals were tortured in order to force a conversion?

Some unfortunates ended up in the Tower of London on trumped-up political charges but I don’t think the Protestant reformers went around from country to country trying to force conversions. However, civil war did result, mainly because of the efforts of King Charles I to introduce reforms designed to return to papal practice (source).

This resulted in the Bishop’s Wars from 1639-1640:

After the Restoration of the Monarchy in 1660, Scotland regained its kirk, but also the bishops. Particularly in the south-west many of the people here began to attend illegal field conventicles. Suppression of these assemblies in the 1680s known as "the Killing Time". After the "Glorious Revolution" in 1688 Presbyterianism was restored.

There were approximately 500 casualties and losses out of a total of 35,000 soldiers (source).

Of greater significance was the War of the Three Kingdoms (which was a civil war) between 1639 and 1651 under King Charles I.

These wars included the Bishops' Wars of 1639 and 1640; the Irish Rebellion of 1641; Confederate Ireland, 1642–1649; the Scottish Civil War of 1644–1645; and the Cromwellian conquest of Ireland in 1649 (collectively the Eleven Years War or Irish Confederate Wars); and the First, Second and Third English Civil Wars of 1642–1646, 1648–1649 and 1650–1651.

Army casualties and losses came to a total of approximately 50,000 English and Welsh and 34,000 others. Also there were 127,000 noncombat English and Welsh deaths (including some 40,000 civilians) (source).

Although religious issues were significant, the resulting civil war did not come under the category of “Protestant Inquisition style tribunals”. I hope that may be of some (belated) help.