I'm working with NRF5 SDK. Most of its source is available (no idea if it's free software or not, but sources are there). The most glaring exception is softdevice - that's BLE implementation, it's huge binary blob, taking control over most CPU.

Their newer SDK based on Zephyr RTOS, I didn't work with it, but I think it's mostly open source as well.

It's all on Github (https://github.com/nordicsemiconductor), but it is not technically open source as it is a modified BSD that does not let you use the SDKs with other chipsets.