Yes - this chart will give you the TASS for a flaps 15 takeoff - but only taking into account the runway length, not the obstacle situation.
You read it like this (there is an example-dashed line in the diagram):
1.) Enter on left with airport OAT - go up until you hit the airport pressure altitude (elevation + QNH correction of 30`per hPa). Then go horizontal to right, until you hit the REF LINE.
2.) Now start on right with field length available, go up to first REF LINE, then follow it PARALLEL to the "slanted lines" for runway slope, then go up again to next REF LINE then follow it PARALLEL to the slanted lines for "head/tailwind", then go straight up (make a long line).
Now follow from the final point of "1" PARALLEL to the "slanted lines" until you hit the vertical long line from 2. From that intersection go horizontal to the right to read off the maximum brake release weight.
If you want to find out the TASS, you need to start the process in reserse. Start with 2.) to get the vertical line. Then go from the right (current weight) to the vertical line, followe PARALLE to slanted lines to the REF LINE (vertical), then go left until you hit the airport pressure altitude then go straight down to read the "theoretical" OAT (=TASS) that would still allow a takeoff with your current weight.
Cheers, Jan