With ASObjC:

Applescript:

use AppleScript version "2.4" -- Yosemite (10.10) or later
use framework "Foundation"

set now to current application's class "NSDate"'s |date|()
set dateFormatter to current application's class "NSDateFormatter"'s new()
tell dateFormatter to setDateFormat:("yyyyMMdd-HHmmss.SSS")
set timeStamp to (dateFormatter's stringFromDate:(now)) as text

However, I don't imagine the clock on your computer will be that accurately set. 

With AppleScript Toolbox:

Applescript:

AST format date "yyyyMMdd-HHmmss.SSS"

Or if you want the Python to spit out the requested formatting instead of doing it in Applescript (Python formatting code is shorter)

Applescript:

do shell script "
/usr/bin/python <<END
from datetime import datetime
now = datetime.now()
print '%04d%02d%02d-%02d%02d%02d.%d' % (now.year,now.month, now.day,now.hour,now.minute,now.second, int(round((float(now.microsecond)/1000), 0)))
END"

This is rounding the fractional seconds to three decimal places (milliseconds) as requested.

If you want the full microseconds:

Applescript:

do shell script "
/usr/bin/python <<END
from datetime import datetime
now = datetime.now()
print '%04d%02d%02d-%02d%02d%02d.%d' % (now.year,now.month, now.day,now.hour,now.minute,now.second, now.microsecond)
END"