This app was mentioned in 2 comments, with an average of 1.00 upvote
If budget is the issue, there are some cheap lavalier mics on amazon/ebay. Buy a Y cable similar to this one on ebay so that you can plug the mics in your phone. For android you can use All That Recorder app (select manual format and set it to 48000k to sync with video).
I have tried recording audio on phones with cheap lav mics and I got usable results. I also tried a shotgun mic with my phones and it did a very good job. Of course I needed to buy a headphone-mic splitter to connect a 3.5mm mic to the phone (just plugging a 3.5mm mic in phone doesn't work). You can get these splitters for couple of dollars on ebay. The phone headsets record sound well, so you can use them too.
Please be aware that you will need to do more work in post (syncing, cleaning up noise, trying to match the qualities between multiple recordings) but it is worth a try if you don't have money to spend.
For android, I tried this app and found it well suited for my needs.
This app let me records USB mics using OTG cable. Worked extremely well.
I don't use iPhone so I don't know any apps but I am sure you can find some good ones.
Good luck.