Thanks for your question.
You may start trimethoprim for cystitis as flucloxacillin may not be very effective for treatment of cystitis.
You do not need to lower flucloxacillin dose while taking trimethoprim.
Do take plenty of fluids to treat cystitis and to prevent dehydration due to diarrhea.
To treat diarrhea due to antibiotics you should take yogurt with live bacterial cultures as well as probiotics to replenish the good bacteria in your gut.
This is my initial answer.Please reply if you need any other information.