So my question is how does the sinad and thd+n ratio and other specs of a dac change an amp, does it override the amps built in audio processing and all that is now handled by the dac? does a cheap amp limit a dac from sounding its best or will buying a higher end amp and using it with the e30 still sound the same as the cheap little kinter amp?
Your E30 DAC interprets and converts the digital audio signal to an analog electrical signal, and it outputs a voltage signal but with little power. The power amplifier's function is to inject sufficient power into this voltage signal to drive your speakers properly, as noted by Frank Dernie and Jimbob54. So the DAC and the amp perform two different functions (except in the case of modern "integrated amps" or receivers, where a DAC is included in the unit), and the DAC therefore does not "override the amp's built-in audio processing".
The E30 performs its signal processing with high accuracy equivalent to audible transparency, so that the signal corruption (quantified by its THD+N ratio, or inversely by its SINAD) in the signal it passes to the downstream amp is imperceptible. The E30 is expected to be used with good amps, and is not designed to compensate for the particular signal corruption introduced by the particular amp it feeds (so its specs do not "change an amp", except that the amp receives a better quality input signal). So the interaction between the DAC and the amp is only the audio signal passed to the amp, and a better DAC changes the audio only in that it passes a less corrupted signal. The amp too is generally not designed to compensate for signal corruption by any particular DAC; as long as the amp operates in its linear range, its operation is indifferent to the nature and quality of its input signal, and it will continue to introduce its own characteristic corruption into the signal. The amp's signal corruption (along with the DAC's signal corruption, if any) is passed on in the signal received by the speakers.
Each link in the audio signal chain receives an input signal and corrupts the signal further, and outputs the corrupted signal which then appears as the input signal to the next link in the chain. So each link has its own THD+N ratio or equivalent SINAD number associated with the corruption it creates in its output relative to its input signal. The acoustic signal output by the speakers will contain the accumulation of the signal corruption introduced by every link in the signal chain, and the overall SINAD of the entire signal chain (treating the entire chain as a single unit, and the corruptions by the links as unrelated to each other) will be less than or equal to the smallest SINAD among all the links in the chain. Equivalently, the overall THD+N ratio between the output and input of the entire signal chain will be greater than or equal to the largest THD+N ratio among all the links in the chain. Essentially, a chain is at best only as strong as its weakest link.
The overall SINAD of a DAC and amp taken together will be less than or equal to the smaller of the DAC's SINAD and the amp's SINAD. The E30's very high SINAD will not override an amp's lower SINAD (if the latter is indeed lower); rather it will be the other way around - the amp's low SINAD will dominate the overall combined SINAD of the DAC and amp. So, in answer to one of your questions, yes, a lower-quality (lower-SINAD) amp will corrupt the signal more and if this corruption is audible, it will limit a better-SINAD DAC from sounding its best. Thus the answer to your next question is that likely the SQ out of your Jamo's could be audibly improved by buying a better amp and replacing the kinter with it (guessing the kinter's audio quality solely from the kinter's price, since I do not know its SINAD and other specs). If you repeatedly upgrade to successively better amps, though, you run into diminishing returns. For example, even using state-of-the-art DAC and speakers, the difference between amps with 100 dB SINAD and 120 dB SINAD would be extremely difficult to hear. As noted by the others, it is most important that the amp's output power be large enough for how loud you want the speakers to sound, and then its SINAD at your normal listening volume is next in importance.
Also if anyone has any recommendations for a speaker amp to buy to go with the topping e30 and my Jamo s803's you could post in the answer to my question budget would be somewhere below $300 USD.
I have no experience at all with speakers or speaker amps over the past many years, so I am ill qualified to make a specific recommendation. A quick search on Amazon yields some decent possibilities:
Fosi Audio HD-A1 Black /
Gold version
S.M.S.L DA-8s
Nobsound NS-02G Hood 1969
Nobsound HiFi Pure Class A Power Amplifier Hood 1969
Nobsound Hi-End Power Amplifier 130Wx2
I am sure there are more similar possibilities and perhaps ones with better performance-to-price ratios. You have to research the pros and cons. There are multiple discussion threads on ASR regarding power amps, that you might find useful. An amp like the Fosi Audio HD-A1 will give you a SINAD of 87 dB (according to the product page), which is more than good enough to clearly bring out the tonality, detail and other SQ characteristics of your Jamo speakers. If you want to chase after high SINAD numbers in amps and approach the E30 DAC's SINAD, it would be a pretty big step up in price from your budget, for rapidly diminishing returns in SQ, and I doubt you would hear any difference in practice with your Jamo's. Several speaker power amps have been measured and reviewed here on ASR by our indefatigable host, many of them multichannel AVRs, and I suggest you check out those reviews.
