Is MIL-PRF-5606 H flammable at 350 deg C?
Both Skydrol and 5606 will burn, though the original 5606 had a much lower flashpoint. However, there are modern derivatives of 5606 such as MIL-PRF-87257 that are within 10-15C of Skydrol's flashpoint and don't suffer the major drawbacks of Skydrol. The US military has switched to MIL-H-83282 which has a flash point, fire point, and spontaneous ignition temperature more than 200°F above 5606.

There are at least 5 flavors of Skydrol (and several for 5606) so it is a bit confusing to generalize "Skydrol" but Skydrol 500B has a flash point of 177 °C (350°F) compared to 5606 at 104°C(219°F). MIL-PRF-87257 very nearly matches Skydrol with a flashpoint of 170°C(350°F).

The two main drawbacks to Skydrol is it is extremely corrosive and much more harmful to human contact. 5606 and it's derivative MIL-PRF-87257 smell nicer and are less likely to attack rubber and plastic. One major disadvantage of 5606 is over time moisture will form condensate that oxidize aluminum tubing. This is one reason aircraft owners are told to regularly fly their aircraft; this prevents long term moisture bubbles eroding a spot in the aluminum line.



source - The US military considers the 5606 derivative MIL-PRF-87257 to more closely meet it's needs than Skydrol.