You needn't give your precise title in your resume. People reading it will not pay much attention to exactly how you title yourself, unless you bill yourself ridiculously, i.e. _Amazing Genius Senior Engineer!_. (In which case you may well be eliminated immediately.) They will look at your background and experience in considering you for hire, not how you title yourself.

If you are indeed a _senior engineer_ , bill yourself as such in your resume. 
Don't say *(senior equivalent)* or *(flat org)* - sounds apologetic or desperate.

Be concerned about presenting your background, your skills and your experience accurately in your resume. Those are the important things - not the title - which can be rather meaningless, as your own experience shows.