There are no special interactions between the spells.
Blur and Invisibility have no special interactions with Slipstream, neither in the rules nor in their descriptions.
There is something to watch out for however.
If they're trying to sneak around invisible while using slipstream enemies can notice the slipstream to figure out there is something happening.
Additionally, here is a relevant FAQ:
What exactly do I identify when I’m using Spellcraft to identify a spell? Is it the components, since spell-like abilities, for instance, don’t have any? If I can only identify components, would that mean that I can’t take an attack of opportunity against someone using a spell-like ability (or spell with no verbal, somatic, or material components) or ready an action to shoot an arrow to disrupt a spell-like ability? If there’s something else, how do I know what it is?
Although this isn’t directly stated in the Core Rulebook, many elements of the game system work assuming that all spells have their own manifestations, regardless of whether or not they also produce an obvious visual effect, like fireball. You can see some examples to give you ideas of how to describe a spell’s manifestation in various pieces of art from Pathfinder products, but ultimately, the choice is up to your group, or perhaps even to the aesthetics of an individual spellcaster, to decide the exact details. Whatever the case, these manifestations are obviously magic of some kind, even to the uninitiated; this prevents spellcasters that use spell-like abilities, psychic magic, and the like from running completely amok against non-spellcasters in a non-combat situation. Special abilities exist (and more are likely to appear in Ultimate Intrigue) that specifically facilitate a spellcaster using chicanery to misdirect people from those manifestations and allow them to go unnoticed, but they will always provide an onlooker some sort of chance to detect the ruse.
Using spells while invisible would also tip off those around them as their manifestations would be noticeable. So while it may be tempting for them to circle around the enemy to get to their backline, this would be noticeable and tip them off that someone is there.