In Cycles, go to the Profile tab and open Settings. Tap on the 'Health' button and 'Turn All Categories On' (or just the categories you want to track). Now Cycles will automatically sync with the Health App.
If this doesn’t work, Health access has been denied and you'll give the Health app access to Cycles. To do this, go to the Health app on your phone and tap your profile picture, then 'Apps', under the Privacy section. Select Cycles and 'Turn All Categories On'.