This is very easy to answer, but it will lead to more questions rather than answering it.
1 ) The profile(s) you having, is probably not exact for the ink you are using, right ?
2 ) The profile(s) you having, is probably not exactly created for the media you are using, right ?
3 ) The profile(s) you having, is probably doesn't make any sense to use on any media, right ?
4 ) The profile(s) you having, is probably the ink profile to media, and nothing to do with your monitor profile, right ?
What you need is to spend about $1000 ore more, to get a spectrometer / colorimeter, and using your Flexi 8.1 profiler to create a color swatch , and using that expensive colorimeter to scan the results, and there you go. Your prints will be PERFECT, everytime!
Flexi Pro comes with Profiler built-in with it. So you can use this function in creating your own profile. The process is simple, it ask you a few questions, and print some testing to see the droplets, ink density, and ink mixture, and then it create like 400+ to 1000+ color chart , and you need a colorimeter / spectrometer to read these chart values. Flexi profiler will convert this color values into their codex for the assigning ICC colors for the printer profile. So your color will never be off again. This profiling will make the Production Manager know how to jet the ink correctly to your particular media that you are profiling on.
That's half of the process.
The other half is to calibrate your monitor, so you can use your monitor profile in conjunction with your ink profile.
You can use i1 monitor calibrator hardware or whatever brand for the monitor calibration, follow its software to do so, then save your monitor profile so that you can call it for simulation at the printing / ripping process via flexi's production manager to achieve exactly as you seeing on your monitor.
However, photo images also do need to assign color profile on to image as well, so there are three profiles you have to deal with.
If you print spot color then these color available with flexi library. Flexi has built-in color standard codex for these spot color such as Oracal vinyl, Avery Vinyl, 3M, Gerber, or even Pantone colors. So you can use these spot color as your control testing on your profile creation since you know exactly what Oracal Red #31 should look like!
Color profile can get really complex, but Flexi has all the resources but you will need a professional colorimeter to be able to accomplish this task.