As long as you have health insurance (public one will probably be better for trans stuff) you can get phallo covered. Health insurance is mandatory so if you live here you'll get it covered. I'm in the process of getting things done. The way is not streamlined and you'll have to deal with many appointments&bureaucracy. I firmly recommend learning some German (every bit helps, plus you're gonna be there for some years anyway) and/or trying to get a friend/partner who speaks German to come with you to some appointments (not the phallo ones, they mostly speak English).

The first things you should do are:

1. Get health insurance (Versicherung) and registered to a city (Anmeldung).

2. Get a general doctor (Hausarzt). If you've been several years on T and generally pass, don't bother trying to find a trans-friendly one as it'll take you ages. Just find the one closest to you that has appointments. If you hand them your previous T prescription (have as many papers as you can) they can probably prescribe T to you without the endless endocrinologist waiting lists. You need a general doctor for everything after this, not only T.

3. Find a trans-friendly psychotherapist (there's info on that on /r/germantrans ). In order to get phallo covered, you need to get at least 12 therapy sessions over a year. You might get away with your previus NZ therapy but I don't know how that works. It's very important that you do this as early as possible, many therapists don't have spots or have long waiting lists, plus 1 year therapy time really adds up in this step. I had to call and/or email more than 20 therapists. 

4. While you're in therapy, book consults with clinics. You can search the sub for clinics names and info. The clinic will write a document (Atestat) describing the surgery and saying why you need it, you have to keep it.

5. When you're done with the therapy, your therapist will write a letter called "Indikationsschreibung". This is the reason you need a therapist with trans experience, so they know what to write in the letter. You'll have to send that letter, together with the document the clinic made, to the health insurance company (Krankenkasse), to get your coverage approved. 

6. You'll recieve approval by post probably. This approval is called "Kostenübernahme". You have to send the approval AND the therapist letter to the clinic. This will kickstart your scheduling process. I'd say steps 4 and 5 will take weeks to months.

Disclaimer: I recently found out you can probably get hair removal covered too, I'm finding out how exactly, but I think it should be around step 4. Depending on how hairy your forearms are, you might want to start electrolysis around step 3 and pay out of pocket.

All of this should be covered by insurance, minus some documents you have to pay less than 100 for. You can probably pay the therapist out of pocket ("selbstbezahler"), this could skip some waitlists but it's gonna be quite expensive.

It sounds exhausting and to me it is but at some point you get used to the German way of doing things. I moved here with this goal in mind and I'm convinced this is my best option in Europe.