@Premysl Cerny, Thanks for posting in Q&A.
Based on my research, since Microsoft Intune is a cloud-based endpoint management solution. It manages user access to organizational resources and simplifies app and device management across your many devices, including mobile devices, desktop computers, and virtual endpoints but there is no such feature in Intune that can obtain and view LogCat/Kernel/System logs from Android devices, but you can try this link mentioned below
https://developer.android.com/tools/logcat
https://github.com/Gegenbauer/CatSpy
Non-official, just for reference.
Or post your issue to Android community to get more help.
https://developer.android.com/community
Non-official, just for reference.
Hope it will help.
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