Can the Macbook Pro drive two Ultra HD monitors at 60FPS each? I'm referring to the 2015 Macbook Pro, 15-inch, with the AMD Radeon R9 M370X with 2GB GDDR5 memory. Can this drive two Ultra HD monitors (3840 x 2160) at 60FPS each? If so, would you be able to simultaneously use the built-in display?

To be clear, I'm referring to SST (single-stream transport) monitors, not MST (multi-stream transport).

You'd have to plug each monitor into a Thunderbolt port, since HDMI supports only 30FPS. Are both Thunderbolt ports on different Thunderbolt buses, or the same? In the latter case, there may not be enough bandwidth.
According to this document https://support.apple.com/en-us/HT204154 The MacBook Pro (15-inch and 17-inch, Early 2011) and later have Thunderbolt2 and can handle two thunderbolt displays (2560x1440).

According to this document https://support.apple.com/en-us/HT202856 The MacBook Pro (Retina, 15-inch, Late 2013 and later) can handle one MST 4K display at 60Hz.

You can run one 4K monitor off of the Thunderbolt display at 60z and a second off HDMI at 30Hz. the two thunderbolt ports are connected. Once you try to connect a second 4K monitor to the other port, you will go over the bandwidth and the second monitor will go dark.