I want to work through this but now I face 2 problems.
1. Can I really accept her saying I can't speak to anyone other than her first on all issues regardless of who is involved or what the issue is. I feel the answer to that is no but how do I approach that considering she has already said she can't compromise on that?
2. How do I actually show her that she is the most important thing to me other than doing something like getting flowers (which I don't think is appropriate anyway)?
Any thoughts/help is appreciated.
I think you will be able to get a lot of good help and suggestions from more communication-skilled board members, so consider this just a start... .

1. Can I really accept her saying I can't speak to anyone other than her first on all issues regardless of who is involved or what the issue is. I feel the answer to that is no but how do I approach that considering she has already said she can't compromise on that?
The short and simple answer to that is of course no... . you can not allow her to put a gag on you and stop you from talking to whom ever you want about whatever you want, whenever you want or need to... . That would be violating your boundaries and your human rights... . So how to go about this... . I think reading and learning a bit of DEARMAN skills would be helpful here. DEARMAN is a tool to get across clearly but without falling into the pit of causing any triggers when delivering what it is you want... . And there are plenty of threads and i think also info texts about it here on this site.
What needs to be very clear when having a r/s with a person who has BPD is that even though they are experts in creating fear in us that we will be tossed out the window if they feel crossed or don't get their will, that can never ever become our responsibility to prevent from happening... . The moment the eggshells come out, the r/s becomes highly dysfunctional and toxic for the non-party. So we have to make sure that never happens... . That means we have to learn to stand our ground when it comes to our personal boundaries. And make them understand that those are rock solid... . Threatening them will for them too jeopardize the r/s... .
I think the toughest thing to learn and to accept when in a r/s with a pwBPD is that we have to allow them to choose whether they want to be in the r/s or not. It has to be their choice at all times, and can never be part of our responsibility to make sure they never want to leave by adjusting our actions and what we say or want or feel to prevent that from happening.
In all honesty I think by doing the eggshell dances and bending and operating out of fear of us being abandoned we too create a mirror to their inner fear of abandonment. And I do believe that if we manage to be more firm calm and steadfast we lessen the risk of them wanting to leave... . By waxing an waining we create an image of ourselves to be insecure and insecure means more risk to them... .
On the other hand, with standing firm and being steadfast also comes the fact that we have to be prepared to accept that the consequence might be that they bail... . But if they do, then they would have done it anyway... . And it will have saved us a whole lot of pain and suffering not having to budge and walk the eggshells and worry constantly about the r/s... .
So how would you go about it? I think you should sit down with her and simply look her in the eyes and tell her you love her, but there is one thing she needs to know about you and that is that sometimes you need to vent stuff that you have on your mind. And that you will make it your business to choose with whom you do it with. Sometimes you will choose to do it with her, but sometimes it is better for you to seek advice or guidance from a friend or someone outside of the relationship, depending on what issue you need to ponder over... . And then formulate something along the lines like: It is important for me to know that I have that freedom within the realm or our relationship to do so, and that you can trust me and my judgement that I never would use that to betray you in any way. I love you, but it is up to you to choose if you can trust me or not. I can not do that for you.
2. How do I actually show her that she is the most important thing to me other than doing something like getting flowers (which I don't think is appropriate anyway)?
I don't think you should fall into the trap of having to "prove" yourself to her, at this point... . I think you need to give her some space to calm down, then sit down with her and have your talk... . if you bend over backwards now and buy flowers or make some grand gestures you will only give here the signal that messing with you like this works and at the end of it there is a reward for it too... . I think it is important not to loose ourselves just in situations like these and give in to our fears of them leaving the r/s... . if we do, the risk of loosing in the end just shoots through the roof... .
But it is not about getting angry or engage into the conflict, but just calmly assert ourselves and explain without too many details where we stand, and give the impression that just as firmly as we stand her, we are also committed to the relationship. Then we create a safer ground for both parties, I believe.
Best wishes
scout99