As Ed Cottrell already stated there is no way to tell, especially if traffic is encrypted.
There is at least one guy who analyzed the traffic over the course of ten hours. He could not find evidence for the sending of any logs. Instead the Kindle only sent the same package over and over again (real logs would change over time).
Most people who claim that data is transmitted to Amazon refer to this thread, which claims that the script /usr/bin/showlogs is "packaging" the data for being sent to Amazon. This script does indeed concatenate old log files. I do however wonder how he makes the connection to logs being sent to Amazon. The results of grepping all files on my Kindle 3 show that there are (at least) two programs that call it:
/test/misc/checklogs.sh strips away most lines in these logs. The information that is left is low level hardware stuff (like "SDIO: sdio_card_irq_put" or register dumps), cronjob notifications (only normal loggers and performance/power, nothing that implies files being sent), daemon start/stops (on reboot), profiling output and several lines about network connections (e.g. Lease of xxx.xxx.0.107 obtained, lease time 604800). All these data is anonymized enough that the only problematic information they could see is, that I jailbroke my Kindle (due to output from the usbnetwork hack).
test/diags/factory/system_diags.sh, which zips the unfiltered log and stores them somewhere where the user can actually see them (comparable to typing ;dumpMessages in the search window).
Of course these are only the occurrences where the script is called from other scripts. They are probably also called from binaries so no one knows.
Here are some lines that could be used to get personal data about you.
#Which books you read (from Amazon, sent via Amazon, copied via USB / downloaded via browser)
140129:134959 cvm[3716]: I Reader:BOOK INFO:book asin=B004UO32XO,file size=1413044,file last mod date=2014-01-01 23.26.34 +0105,content type=ebook,length=MobiPosition_ 218620,access=2014-01-29 13.50.50 +0105,last read position=MobiPosition_ 25308,isEncrypted=false,isSample=false,isNew=false,isTTSMetdataPresent=true,isTTSMetadataAllowed=true,fileExtn=azw:
140109:205652 cvm[3716]: I Reader:BOOK INFO:book asin=BTPHGRQ6BAGPRU4M3JPCR4PV2DNNPBZO,file size=1101110,file last mod date=2013-08-11 14.27.56 +0103,content type=ebook,length=MobiPosition_ 2372225,access=2013-12-25 10.10.18 +0103,last read position=MobiPosition_ 1090739,isEncrypted=false,isSample=false,isNew=false,isTTSMetdataPresent=true,isTTSMetadataAllowed=true,fileExtn=azw:
140129:135140 cvm[3716]: I Reader:BOOK INFO:book asin=unknown,file size=153384,file last mod date=2014-01-02 19.10.24 +0105,content type=ebook,length=MobiPosition_ 241149,access=2014-01-29 13.54.55 +0105,last read position=MobiPosition_ 6251,isEncrypted=false,isSample=false,isNew=false,isTTSMetdataPresent=false,isTTSMetadataAllowed=true,fileExtn=prc:
#KPDFviewer started via kite behaves like a real pdf
140129:135452 cvm[3716]: I Reader:BOOK INFO:book asin=unknown,file size=716,file last mod date=2013-04-16 23.29.58 +0105,content type=ebook,length=0.0 (0 1) _ -1_ -1 0,access=2014-01-29 13.49.42 +0105,last read position=0.0 (0 1) _ -1_ -1 0,isEncrypted=false,isSample=false,isNew=false,isTTSMetdataPresent=false,isTTSMetadataAllowed=true,fileExtn=pdf:
#Which books are in which collection (including collection name)
140102:191934 cvm[3716]: I NamedCollectionImpl:AddingItem:collection=Fachbuch,asin=null,itemHash=-762173641:String
#When you open a book, pressed buttons (flip pages) or went to the home screen
140129:134959 cvm[3716]: I Reader:BOOK INFO:book asin=B004UO32XO,file size=1413044,file last mod date=2014-01-01 23.26.34 +0105,content type=ebook,length=MobiPosition_ 218620,access=2014-01-29 13.50.50 +0105,last read position=MobiPosition_ 25308,isEncrypted=false,isSample=false,isNew=false,isTTSMetdataPresent=true,isTTSMetadataAllowed=true,fileExtn=azw:
140109:205700 cvm[3716]: I FrameworkKeyEventDispatcher:USER_HARDKEY_PRESS:KeyPressed=Right_PrevPage:User pressed Right Side Turn Prev Page button
140129:135609 cvm[3716]: I GUIManager:HomeViewSwitch:view=CollectionView:
#Battery parameters and temperature (even display temperature)
140129:135721 powerd[2442]: I def:battinfo:cap=58%, mAh=831mAh, volt=3835mV, current=317mA, temp=82F, bp=3835mV, lmd=1443mAh, cycl=1, cyct=12:
140129:135302 eink_fb: I bs_cmd_ld_img_upd_data_which:def:temp=31C:from pmica
#That you searched (not what!)
140129:135856 cvm[3716]: I Search:COMPLETED:milliseconds=2150:
Except for how slow you read, when you use the browser (which sites you browse is not included) and how warm it is where you are (inside/outside?) there are barely personal information. Even the books are only identified if you received them via Amazon. If they would use it, why would they ask me to rate a book I have not yet started to read.
The data may be useful to spot things like "The display is damaged and you used it at -40°C" and for troubleshooting and debugging, but not for a real analysis of what you read.
Of course there can always be binary programs that collect more information and send them. And even if they are not there, Amazon could ship them with the next update. Nobody knows for sure, but this is the same for any ebook reader, tablet, phone and even pc.
