Being a transwoman, I have plenty of experience with dysphoria, but I can only imagine what is like to be gender-fluid, shifting back from one gender identity to another over time and circumstances.
That said, the most important thing you as a partner can do is:
Affirm your partners gender whatever it is at the time
This harder than it sounds because it is preferred that all possible genders get a fair share of appreciation and affirmation. Also, you are the person that they wake up next to in the morning and you must intuit, possibly based on non verbal cues such as facial and body posture, what the gender of the day is before they have had time to work on their gender expression. It helps tremendously when there is at least one person who gets it right most of time.
Work with them on their gender expression
Social dysphoria results from social interactions where people treat you differently from the way you are at the time. This is unfortunate because most people will be unable to guess unless you look and act the part, especially when the current gender does not match your partners physique. Get a big wardrobe and fill it with clothes that allow them to choose to wear something that fits the current gender identity, not just the dominant one. As a partner help picking out stuff, but be honest and say it if it does not suit them. Compliment them on their attire in a gender affirming manner (e.g. 'sharp threads, dude' or 'you look lovely in that dress'). Occasionally, give feedback on mannerisms (e.g. 'if you curve your hand like that it looks quite feminine but if you hold it straight it looks more manly')
Tell them that you love them no matter what gender they are
This hardly needs explanation except that this goes for intimate moments and sex too. And from my experience this is where the body dysphoria can kick in big time. Talk about this with them and really listen to their body reaction.
Discuss physical changes
Body dysphoria is caused by the physiology of the body not matching the identity. It kicks in when you look in the mirror or when you touch yourself or are touched by someone else especially in the genital areas, but also the face. It is also tied to some physiological functions. Imagine how frustrating it can be for an AFAB to identify as masculine and have your menses at the same time.
Cosmetic changes can help reduce some of that, e.g. tucking for AMABs and binders for AFABs, hairstyle, makeup or lack thereof and so on. I certainly feel less dysphoric after applying makeup but this is also a matter of personal preference and cultural background, not everyone is the same.
But sometimes it is not enough and some more permanent changes are called for. These can range from permanent facial hair removal, partial Hormone Replacement Therapy to operations such as plastic surgery. You, as a partner, can be open to discuss these options and assist in finding medical professional help. Keep in mind that these changes are permanent and should be such that such procedures make it easier to shift. Medical treatment for gender-fluids with severe body dysphoria is still in its infancy, however.
Don't lose yourself
Don't make them your project. You are a person, they are a person, you are equals. Live it together.