I’ve looked into this before, and it really depends on the type of RFID they use. Older versions have been cracked, but newer ones can’t be copied over (easily or at all).

If your company is serious about security, you will not be able to put the content of the card on your phone. What newer, more secure versions of RFID do is receive a code from the reader system, replies to it internally, and then sends back the answer. Even if you try to copy this over, you will not be able to open the doors of your facility.

I think the first step should be to use one of these apps that can read RFID and see what protocol your card uses. If it’s an unsecure one (i.e., only pushes out a code and checks it in their database that it’s yours), you could probably try to copy it over. However, if it’s not, you could also just dissolve the card with some acetone and place the resulting wires in your phone’s case, near the bottom. Like that, it shouldn’t interfere with your phone’s NFC, as that one is usually next to the top area of your phone.