Can you cast a spell for its flashback cost while it is in the graveyard and still use kicker?

Flashback allows you to cast a spell from your graveyard by paying its flashback cost instead of its mana cost (CR 702.34a). Kicker is an additional cost you may pay when casting a spell (CR 702.32a). These two mechanics are independent and can be combined.

When you cast a spell using flashback, you are still casting that spell — you simply use the flashback cost in place of the mana cost. Because you are casting the spell, all additional costs, including kicker, are still available to you (CR 601.2b). Paying a kicker cost is optional, so you choose whether to pay it at the time you declare the spell and its costs.

The key rule is CR 601.2b: after choosing the spell to cast, you may choose to pay additional costs. Kicker is an additional cost, so it is available regardless of what alternative cost (like flashback) you used to cast the spell.

Concrete example: You have Voidslime... actually, consider Rite of Replication (flashback doesn't exist on it, but for a clean example): Suppose a card has Flashback {4}{U} and Kicker {3}. When you cast it from your graveyard using its flashback cost of {4}{U}, you may also pay the kicker cost of {3}, spending {4}{U}{3} total, and the spell will have been kicked.

After the spell resolves, it is exiled rather than going to another zone, as is normal for flashback spells (CR 702.34c). The kicker effect still applies fully to the resolution of the spell.