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My party and I are flying on the back of a large undead creature (homebrew) to go extended distances. It has a speed of 50, so we estimate that if it moves and dashes as an action it gets 100ft per round, or ~11.37 mph.
What spells or other abilities would be able to cause a significant difference in its ability to travel faster? The party is 7th-8th level.
A spell such as haste only provides an extra ~half mile per cast, so we need something that is a better rate.
The target's speed increases by 10 feet until the spell ends.
Ten feet per round may not seem like much, but this spell has a great duration of one hour and is only first level. Even a fourth level caster, if you are willing to upcast with higher level slots, can use it for seven hours a day, or nine hours if they have arcane recovery or natural recovery. Applied over an eight hour march, and with your method of calculating speed, that nets you more than 18 extra miles of movement.
However, you should be aware that your DM may not be calculating your overland speed based on encounter speed. The PHB has rules for travel pace in miles per day irrespective of the speed of the traveler, but these assume "relatively simple terrain", travelers that will need to rest, and travelers that cannot move indefinitely at their dashing speed. Given you have a flying undead mount that is likely immune to exhaustion, your DM may apply the Special Travel Pace (DMG 242, 242) as noted by Darth Pseudonym. Following these, "In 1 hour, you can move a number of miles equal to your [non-dashing] speed divided by 10" and "For daily travel, multiply your hourly rate of travel by the number of hours traveled (typically 8 hours)" and "For a fast pace [which gives you a Penalty on Perception checks while traveling], increase the rate of travel by one-third."
Putting all of this together, your flying undead mount has speed of 50, thus moves at 5mph, and can cover 40 miles in a day, or c. 53 miles if moving at a fast pace. With eight applications of longstrider, this would increase to a speed of 60, 6pmh, 48 mpd, or 64 miles in a day moving fast, boosting your travel by nearly eleven miles (with each application of longstrider netting you a bit more than a mile as bonus travel).
As a bit of a frame challenge, suppose you wanted to move fast overland, and there was a spell that let you move faster - but not by making your undead mount fly faster. Rather, by making you move so fast that your undead mount is the slowest member of your party, and could actually be abandoned.
Phantom Steed creates a mount for you, and one that will let you move 13 miles an hour at a fast pace, which is more than double your undead mount, even with a longstrider on it. Phantom steed lasts an hour, but it is third level, so your 7th level wizard caster can get in four castings a day with an upcast (or up to 6 a day with an 8th level caster and arcane recovery).
However, unlike your undead mount, you will need a phantom steed for each party member - so even the four castings you can do at 7th level will last only an hour for a party of four - if they are hard cast. Phantom Steed is also a ritual spell, though - which means you can cast it without spending spell slots, and without even preparing it. But here's the tricky part - each steed you make will take 11 minutes, and if you want the party to travel together, you won't be able to leave until you have made steeds for everyone.
With a small party of three, it would take you 11 minutes from "start time" to make one steed, 22 minutes to make two, and 33 minutes to make the third. However, if you start immediately after completing the third, you will have only 38 minutes left to travel, since the steeds last only an hour and your first steed is at that point already 22 minutes old. Traveling at 13 miles an hour for those 38 minutes, the three of you together can cover 8.2 miles. In the same amount of time it took you to do that (71 minutes; 33 minutes to make the three steeds and then 38 minutes of traveling), your flying undead mount would have traveled 5.9 miles. Since casting the steeds as rituals cost you no spell slots, at the time the first one disappears you can begin the process over again, and thus cover much more ground than you could on your mount.
As you can see, there are diminishing returns to this. If you need to make four mounts for your party, then you will spend 44 minutes making them, and have only 27 minutes left to travel because the first mount is by then 33 minutes old. With four steeds, you would cover 5.85 miles before needing to recast, whereas your flying mount could still cover 5.9 miles in those 71 minutes. With greater party numbers your travel time and distance covered continues to diminish.
However, you can still hard cast to get a boost. Perhaps your party of four all gets steeds for the first hour with four casts in four minutes, and then ritual casts all the others. Or maybe you ritual cast three and then throw in a hard cast for the fourth person each time. The steeds are actually creatures, so you can cast longstrider on them as well for a further boost.
While not available at your current level, if you have a druid, at 11th they will be able to access wind walk, which is far superior to your undead mount and the phantom steeds.
Related: What is the farthest someone can travel in 8 hours without teleporting? has several answers with combinations of tricks. Such as giving the creature a Transmuter's Stone set to +10ft move speed. Pick any that your party could use.
Polymorph is a 4th level spell, so your party can only do this for a couple hours per day (burning a top-level spell slot each time). It can be combined with Longstrider (1st) as Kirt suggested, to go even faster.
Beasts with a move speed of at least 70:
A huge beast could carry a whole party on one creature.
Polymorph can change into a beast of CR less than or equal to the original level or CR of the creature. Wild Shape has lower CR limits, CR1 for non-moon druids, or CR=level/3 for moon druids. But either way, no flight until 8th level. A CR1 moorbounder could be a useful option if there's good terrain. (Or if you have a ranger who can let the group ignore difficult terrain in their favoured terrain.) A druid has to have seen a creature to wild shape into it. Polymorph has no such requirement, so presumably just knowing of the creature, or imagine it, or whatever your DM decides.
You can only poly or wildshape into a "beast", so presumably it would tire during flight, unlike an undead which can potentially dash every turn because undead don't tire. (The chase rules on p252 DMG say you have to start making con checks for exhaustion if you dash for more than 3+Con rounds in a row.) An undead polymorphed into a beast would probably still experience the beast's endurance limits.
In Critical Role's campaign 2, Matt Mercer let the party of 6 or 7 travel by polymorphing two members into giant eagles who carried the rest. So 2 passengers per eagle, or 3 on one with the lighter party members. I'm not sure how he calculated travel speed, but he did mention encumbrance of the eagles being a factor. With it being worse for Giant Owls (the night option: CR1/4, fly 60, Large but str 13. But with Stealth +4, and 120ft darkvision.)
(The Might Nein never bothered to optimize their logistics by polymorphing the heaviest 2 members. Instead usually having the casters polymorph themselves, which required carrying a Firbolg and an Aasimar barbarian)
Other Huge beasts that can carry more of the party at speeds higher than normal 30ft walking, and let the whole party's speed be boosted with one casting of Longstrider:
If a mundane Mammoth is bigger within the Huge size category than a Giant Elk, it might be easier to strap more of your party onto their back without reducing their speed. Up to the DM on that one. Also an issue of the party knowing of the existence of different types of beasts.
You asked for spells, but this is at least worth mentioning. At 6th level, if they choose Elk:
Elk. Whether mounted or on foot, your travel pace is doubled, as is the travel pace of up to ten companions while they're within 60 feet of you and you're not incapacitated. The elk spirit helps you roam far and fast.
This looks like it should apply when the whole party is riding on the back of a large or huge flying mount. Or at least a ground mount such as an actual Giant Elk.
A Ranger with the right Favored Terrain selection can let the group ignore difficult terrain when travelling.
In general, see What ways are there to increase travel pace each day for a group exploring? for mention of this, and some spells like Wind Walk.
Your party isn't high enough level for this, but this is the go-to spell for fast travel that doesn't skip the intervening distance. Like polymorph, it's not adding speed: it's replacing their movement with a different faster one.
You and up to ten willing creatures you can see within range assume a gaseous form for the duration, appearing as wisps of cloud. While in this cloud form, a creature has a flying speed of 300 feet and has resistance to damage from nonmagical weapons. The only actions a creature can take in this form are the Dash action or to revert to its normal form.
(Reverting also takes 1 minute, during which you're incapacitated, so don't scout into dangerous situations.)
It's magically powered flight, so you can dash every turn without exhaustion. The travel rules cover it specially.
