They say the hardware will use an i.MX6 or i.MX8 SoC, which I assume implies they are using the Freescale/NXP SoCs. i.MX6 isn't really intended for use in phones (afaik) and I don't know of any recent phones which use i.MX6 in them. i.MX8 isn't publicly available yet, but possibly they could leverage some other vendor's hardware phone design using i.MX8.
However, based on the schedule they show in the pledge info, they already have the "PureOS I (CPU)" step mostly completed and they plan to be booting the hardware before the end of 2017, so this seems to make i.MX8 unlikely imho.
Some Kindles may use i.MX6, likely simply because some i.MX6 versions have an integrated e-paper drive subsystem which avoids the need to use an external e-paper controller. I believe early Kindles used the Epson e-paper drive controller.
However, based on the schedule they show in the pledge info, they already have the "PureOS I (CPU)" step mostly completed and they plan to be booting the hardware before the end of 2017, so this seems to make i.MX8 unlikely imho.