Move speed increases with specific speeds

[sleek orbit]

Sometimes special movement speeds are listed as being equal to your walking speed (E.G. Beasking Avian Fly Speed, Ranger's Climbing or Swimming speed) while others are listed as giving you a speed with an explicit value (E.G. Windborn Elemental Scion's 10ft fly speed or the Shifter Druid's Elemental Infusion feature granting 90 ft flying or swimming speed or 30ft burrowing speed).

When you have a special movement with an explicit speed, are these affected by features that increase movement speed by X amount, such as a Monk's Unarmored Movement or a Barbarian's Fast Movement, or are those abilities intended to only affect the base movement/walking speed, and with it only increases Special Movement speeds if they are "equal to your walking speed"?

[minor gust]

To be clear, this is for the Black Flag system and Tales of the Valiant, yes?

[sleek orbit]

Yes

[floral garnet]

This is a clarification arriving in the upcoming errata update, but effects like Fast Movement and Unarmored Movement specifically affect walking speed. This means they can affect anything based on walking speed, such as an avian beastkin's flying speed. Lineages that grant special methods of movement will almost always grant one based on the character's walking speed, as seen in the beastkin.

If an effect has a specific value for the speed, that can't be changed except by effects that change any/all speeds, such as the longstrider spell. This means that an avian beastkin barbarian's Fast Movement can increase its natural flying speed, but a kobold monk's Unarmored Movement doesn't increase the flying speed it gains from the fly spell.