OK first let me say that I am a beginner in SFQ and I don't speak on behalf of anyone - this is just my opinion. I do by the way practice chinese martial arts.
There are different types of qigong, some a martial and some are not. SFQ is a healing and cultivation method. It's not part of any style, and there are many healing/cultivation qigong teachers out there doing things that are not part of any martial style. How your teacher got the idea that all qigong is related to some martial style is not clear to me. I suspect you misunderstood your teacher. It seems strange and I can tell you definitively that most qigong is not associated with any particular chinese martial style.
From the point of view of SFQ I will say that Chunyi Lin says not to mix SFQ with other qigongs and to wait 30 minutes after doing SFQ if you want to do something else so I would say leave a 30 minute interval between chen taiji and SFQ if you want to do SFQ.
There is a form of qigong that goes with chen taiji and I believe it is called hunyuan qigong. Do a search for hunyuan qigong and see what comes up - I think the teacher is located in canada.
I have found SFQ to be particularly valuable in terms of healing. It's not taiji ruler or iron shirt and it's not meant to be. If you want those things they are out there and chunyi lin recommends getting several years experience in one primary qigong method before doing other things. In the level one manual Chunyi Lin advises people to stick with a particular qigong if it's working for them. If not or if they're looking for something he will of course recommend SFQ.
I will sum up with the following - SFQ will help your whole life. You get benefits from the beginning. It's not the first qigong I have learned but it is the most powerful as far as healing, balance, and wellness goes. I have pleanty of time to do chinese martial arts when I'm not doing SFQ.
I hope I have not offended you with my answer. I wish you the best.
