In Acts 25:10 Paul appeals to Caesar. What aspect of Roman law/citizenship was he invoking? Some commentators claim it was provacatio, others amplius. Most commentators simply state he had the right to appeal but what exactly was he invoking?

The wikipedia article on Valerian and Porcian law provides support for Paul's right to not be flogged as an interrogation technique on a separate occasion. But not for appeal to Caesar. 

Edited: for clarity.
SUMMARY
It was provocatio, not amplius.  The latter was used by Felix to delay judgment.  From R.C. Sproul's 2010 commentary on Acts page 392 on Acts 24:22:

Here Felix invoked the Roman principle known as amplius, the formal delay or reservation of a final judgment.  Paul was not convicted in front of Felix, but Felix delayed a final decision on the matter and ordered that Paul be bound over to prison to await further examination by Lysias and then a final decision by Felix.

Appeal to Caesar WAS indeed part of a Roman Citizen's right, affirmed by a later law Lex Iulia de vi publica et privata promulgated in Augustus' reign before the birth of Jesus and was still in effect by the time of Paul.  See IV. Excursus: The Appeal under the early Emperors chapter of the 2010 book The Trial of St. Paul: A Juridical Exegesis of the Second Half of the Acts.  Quote from page 146:

... Indeed the right to appeal was re-affirmed by the promulgation in Augustus' reign of the Lex Iulia de vi publica et privata.  This law basically forbade an official holding the imperium to bind, torture, or kill a Roman citizen who had appealed to Rome.  The importance of the Lex Iulia de vi publica et privata lay in the fact that from the date of its promulgation &quot;the Roman citizen was protected throughout the Roman Empire from the capital jurisdiction and violent coercitio of provincial governors.  ...

DETAILS
There is a very well researched article (with scholarly citations), The “Judicial Adventures” of Paul the Apostle, that shows how Luke used precise legal and Roman government terminologies contemporaneous with the middle 3rd of the 1st century, which indirectly bolsters the traditional dating of the book of Acts, because in less than 50 years the process changed.
The article covers ALL of Paul's entanglement with Roman law in the book of Acts and explained 1) how he acquired and used his citizenship for his advantage, 2) how different Roman cities have variations in judicial avenues because of local vs. empire rule, 3) how different types of governorship were in place, along with the scope of their authority, 4) how the whole city could be punished if they mistreat a Roman citizen, 5) the precise type of Roman law applicable to Paul's case in which he appealed to Caesar, but most importantly how it turns out that some scholar attributes to the Book of Acts the only surviving &quot;court transcript&quot; of a provocatio (appeal to the emperor) proceeding of that era before the process changed.
Some quotes from the article:

Privileges of Citizenship
The closest modern analogy that we can draw to the privileges of Roman citizenship might be the English under the British Raj20 or Americans abroad during the ﬁrst half of the Twentieth Century. Perhaps chiefest among their rights were those in the judicial sphere, especially the right provocatio, or appeal to the emperor. About two decades before the birth of Christ, Rome passed a law, the lex de ui publica, which

forbade any magistrate to kill, scourge, chain, torture, or even sentence a Roman citizen who had announced his intention to appeal, or prevent him from going to Rome to lodge his appeal there within a ﬁxed time.21

The only known statutory exception to this rule deals with citizens who were in military service. Over such troops (as well as all others) gov­er­nors and generals held the ius gladii, the power of execution; it was considered necessary for military discipline.22
...
The Trial Before Festus (Acts 24:27-25:12)
Paul’s trial before Festus is interesting literarily as well as legally. Up to this point we have compared Luke’s accounts against known and little-known history. Now the tables are turned and Luke becomes a legal benchmark of sorts. As legal scholar A. H. M. Jones sees it, Paul’s trial before Festus is “the only account we possess of a provocatio…” (emphasis mine).49 That is, while others write of the process generally, or mention cases wherein provocatio was employed, we have no “court transcripts” other than Luke’s to show the “nuts and bolts” of the procedure.
The three elements of the extra ordinem session are present even more clearly here, for Festus’ consilium is mentioned by name in Acts 25:12.50 The circumstance that triggers Paul’s appeal to Caesar’s tribunal lies just beneath the surface of our English text. Festus is torn between two things: on the one hand, simple justice (Luke points out that the Jews brought charges “which they could not prove,” v. 7); and on the other, political expediency — as the new governor, he “wished to do the Jews a favor” (v. 9). Bruce believes that back of this was the im­pli­ca­tion that Festus “might treat the San­he­drin as his consilium”51 if the venue moved to Jerusalem. Thus, while perhaps win­ning Festus a “political honeymoon,” it would hardly have been an even-handed affair. Hence, after over two years of conﬁnement, Paul appeals to Rome.
Luke’s record of the fact that Paul chose to appeal helps to date his work and sources, for less than ﬁfty years later the process had changed. As Bruce states it:

By the beginning of the second century a.d. it evidently became the regular practice for citizens in the provinces, charged with offenses not covered by statute law, to be sent to Rome almost automatically, without having to take the initiative in appealing to Caesar.52

Once again, the record of Paul’s “judicial ad­ven­tures” is on target.
Endnotes:
2. Mark Black, “Paul and Roman Law in Acts”, Restoration Quarterly: Studies in Christian Scholarship, (1981) 209.
4. A. N. Sherwin-White, Roman Society and Roman Law in the New Testament, (Baker Book House: Grand Rapids, MI, 1963) 1. I am indebted to Sherwin-White for the phrase “Judicial Adventures” which inspired this article's title.
9. Francis Lyall, “Roman Law in the Writings of Paul — Aliens and Citizens”, The Evangelical Quarterly, (48) 12.
20. Lyall, “Roman Law”, 10. This paints quite a picture for those with some familiarity with British India!
21. F. F. Bruce, New Testament History, (Doubleday &amp; Company, Inc: New York, 1969) 358
22. Black. “Paul and Roman Law in Acts”, 211. It should be noted that the point is still debated. C. E. Brand, a U.S. Army military lawyer, in his book Roman Military Law, points out that the dispute is fueled by a coin inscription and how it is interpreted. Brand does not ﬁnd the idea of a condemned soldier’s right to provocatio very logical — or appealing. See especially pp. 67-68. Still, he feels that a citizen-soldier’s rights were valid when involved in non-military judicial disputes.
49. A. H. M. Jones, The Criminal Courts of the Roman Republic and Principate, (Rowman and Littleﬁeld Publishers: Totowa, NJ, 1972) 101. Curiously, after making this statement, Jones goes on to say that it “is unfortunately very confused, and one is led to suspect that neither Paul nor his biographer understood the legal position…”! If it is our only example, as he insists, how does he know that Paul and Luke were “confused”?!
50. And knowing of the existence and necessity of the consilium, we are not likely to confuse it with the other “council” mentioned in Acts 4:15 and 24:20, when it clearly refers to the Sanhedrin's council.
51. Bruce, History, 357.
52. Bruce, History, 358.