Look for the proper devel
package:
$ cygcheck -p "sys/termios.h"
Found 11 matches for sys/termios.h
cygwin-devel-3.0.7-1 - cygwin-devel: Core development files
...
cygwin-devel-3.1.7-1 - cygwin-devel: Core development files
cygwin-devel-3.2.0-0.1 - cygwin-devel: Core development files
...
install the cygwin-devel
package where all the cygwin headers are included
$ cygcheck -c cygwin-devel
Cygwin Package Information
Package Version Status
cygwin-devel 3.1.7-1 OK
$ cygcheck -l cygwin-devel |grep termios
/usr/include/termios.h
/usr/include/machine/termios.h
/usr/include/sys/termios.h