How do we know that gluons travel at the speed of light? Since gluons are located within nucleons and immediately outside of them, how do experiments determine parameters like their speed? Is it possible we could be assuming they travel at the speed of light since they are massless, but in reality they travel faster/slower than light?
 A: Gluons, like quarks, are bound inside nucleons. However, it's not quite correct to think of either quarks or (especially) gluons as being little particles inside a nucleon. Before addressing questions about their speed, it's important to appreciate the limitations of the idea that they are particles — or classical waves, or anything else to which we might normally apply a concept like "speed".
Quantum chromodynamics (QCD) is expressed in terms of quark and gluon fields, not particles. Particles are phenomena that the model predicts when the conditions are right.  The only particles that QCD predicts under ordinary conditions are mesons (like pions) and baryons (like protons and neutrons), both of which are "color neutral". In that context, I don't know of any natural sense in which qualities like "speed" can be attributed to individual gluons, because I don't know of any natural sense in which a meson or baryon is made of individual gluons! Mesons and baryons are a different kind of structure composed of quark and gluon fields. Even the usual cartoon of a proton being made of two up-quarks and a down-quark isn't quite accurate. It's good enough for some purposes (like the Bohr model of the atom), but a proton is more accurately described as a quantum superposition of many different combinations of quarks (and gluons), like three up-quarks and one anti-up-quark and a down-quark. 
One of the most direct manifestations of individual quarks and gluons is in a phenomenon called jets. This phenomenon occurs, for example, when an electron and positron (anti-electron) are smashed together with a center-of-mass energy between about 5 GeV and 45 GeV (the GeV is a convenient unit of energy is particle physics; it stands for "giga electron volts"). In this energy range, the result is often two back-to-back "jets" of hadrons (mesons and baryons). QCD predicts that this will occur as the result of the electron and anti-electron annihilating each other and producing a quark and anti-quark moving away from each other in opposite directions. But since quarks (and anti-quarks) are confined under ordinary conditions, they don't get very far before they become "clothed" with other quarks and gluons, resulting in two back-to-back jets (bunches) of many color-neutral particles instead.  
At the higher end of this energy range, above about 20 GeV, we occasionally see three-jet events, with three jets of color-neutral particles propagating away from the point where the electron and anti-electron annihilated each other. This is also predicted by QCD, which describes it as the creation of a quark, and anti-quark, and one gluon, all initially flying away from each other. This can't last for long, though; they quickly "clothe" themselves with other quarks and gluons, resulting in three jets of color-neutral particles instead.
(By the way, to check these things while I was typing them, I referred to page 24 in chapter 1 of Renton's book Electroweak Interactions. But I still accept responsibility if I've said anything inaccurate.)
So, how fast does a gluon move? Well, considering the high energies involved in the collisions that produce these jets, the final particles tend to be moving away from the collision point at very nearly the speed of light, even though most of them have mass. I'm not sure the "bare" gluon lasts long enough to really constitute a well-defined particle (maybe an expert can chime in and quantify this — or correct me if I'm wrong), in which case the concept of "speed" is once again not quite appropriate.
So, do gluons move at the speed of light? Before we can answer that in a meaningful way, we have to find a condition under which  gluons exist as individual particles long enough for the concept of "speed" to make sense... and that's not as easy as it sounds.
A: This is complementary to the answer by Chiral Anomaly, extending it:
At extreme energies in particle interactions, QCD predicts quark gluon plasma:

A quark–gluon plasma (QGP) or quark soup is a state of matter in quantum chromodynamics (QCD) which exists at extremely high temperature and/or density. This state is thought to consist of asymptotically free strong-interacting quarks and gluons, which are ordinarily confined by color confinement inside atomic nuclei or other hadrons. This is in analogy with the conventional plasma where nuclei and electrons, confined inside atoms by electrostatic forces at ambient conditions, can move freely.

This at the moment is studied in ion collisions at the LHC:

For a few millionths of a second, shortly after the Big Bang, the universe was filled with an astonishingly hot, dense soup made of all kinds of particles moving at near light speed. This mixture was dominated by quarks – fundamental bits of matter – and by gluons, carriers of the strong force that normally “glue” quarks together into familiar protons and neutrons and other species. In those first evanescent moments of extreme temperature, however, quarks and gluons were bound only weakly, free to move on their own in what’s called a quark-gluon plasma.

.....

Jets are “hard probes”, by nature strongly interacting but moving so fast and with so much energy that they are often not completely absorbed by the surrounding quarks and gluons in the quark-gluon plasma. The degree of jet quenching – a figure that emerges in data from millions of collision events – plus the jets' orientation, directionality, composition, and how they transfer energy and momentum to the medium, reveal what’s inside the fireball and thus the properties of the quark-gluon plasma.

One has to realize that particle physics is a mixture of theory and experimental validation. The validation of QCD at low energy, which has the analogue of the photon, called a gluon, with a zero mass and thus limited to the fixed velocity c of special relativity , hypothetically, because it cannot be measured in the lab, only the consequences are measured : mesons, baryons, jets ... which validate the QCD model quite well . A QCD model with  a  massive gluon would not fit the data in any way.
But as the theory is asymptotically free, more data come from high energies where in a plasma quarks and gluons can be  modeled as particles, and as of the present, the zero mass of the gluon is validated by data at  the LHC because QCD predictions fit the data, and by observations of the quark gluon plasma state of the early universe, which also can be modeled by asymptotically free quarks and gluons.
The basic point is that one trusts the mathematics in the model , if one cannot measure directly the hypothesis, and checks the hypothesis by fitting data, which validate the model . In this sense a measurement at second (third fourth ... as there are integrals involved) hand.
