I would like to order primers to amplify 5' regions of few genes starting directly below transcription promoters but I'm wonder how accurate are the experimental data in DBTSS (http://dbtss.hgc.jp/). Is there any alternative to it?
Yes there are some other alternatives. Have a look at this page that summarize them at molbiol-tools link down here.
If you are very concerned about validation I would suggest EPD database. It is manually curated (but has not whole genome coverage). If you do not find your promoter in EPD, have a look at EPDnew (at the same website)
The UCSC genome browser also has TSS available – you can download the TSS for a given genome or view using the browser. Some pointers on how to do it here: http://redmine.soe.ucsc.edu/forum/index.php?t=msg&goto=4952&S=d0e02860cb02957fa59ba53d572fa706