Maybe some of this would be more fitting as a comment, but I'm too new to make those, so I'll write more in-depth for an actual answer.
First off, the climate. Finland is nowadays mostly Köppen type Dfc (Subarctic), with the southern/southwestern coastal areas being Dfb (Warm-summer humid continental). Slash-and-burn may have been practiced throughout Finland in prehistoric/early medieval times, but it seems likely it would've been supplanted by more modern agricultural methods fairly early in said coastal areas, both due to a more favourable climate and due to more contact & trade with other peoples, as well as higher population densities. The Lenape lived in the coastal and near-coastal areas of modern-day Delaware, New Jersey, Pennsylvania and New York. The climate there now ranges from humid subtropical climates (Cwa) to hot- or warm-summer humid continental (Dfa or Dfb respectively). So there's certainly some overlap.
Continuing for a bit longer with the climate subtopic, the 1600s were also part of the so-called Little Ice Age, during which temperatures were 2-3° C (3-5° F) lower than the long-term average. This wasn't a global event, but did affect most of the Northern Hemisphere, including Finland and at least the NE coast of North America. A colder and more unpredictable climate could have caused an increased in the popularity of older, lower-yield but perhaps more reliable (at least in poor soils) farming methods.
Moving on to the type of forest: both have at least some amount of mixed woodlands, with the US coast perhaps leaning more towards deciduous forests and non-coastal Finland towards coniferous trees in mature forests, but keep in mind that long-term use slash-and-burn agriculture will cause the proportion of deciduous trees to increase since especially birch, willow, aspen and alder all colonize clearings such as clear-cuts and former slash-and-burn fields quicker than conifers do.
So there's some similarity, but not complete parity, in terms of climate and possibly in terms of which kind of forests were used for slash-and-burn. Regarding the Finnish techniques, there were 3 main styles. The original one was to use deciduous, or deciduous-heavy mixed forest, and fell the trees a year before they were to be burned. The main crop was rye (for bread), sometimes barley (for beer and bread). Another type was to just fell and burn during the same spring, this was used for barley, turnips and flax. The third and newest style was adopted from Finnic peoples in Northern Russia due to being the only style suitable for nearly pure conifer forests. This is maybe the one dominating the public image on slash-and-burn in Finland: it involves burning a coniferous forest, and pretty much only rye would be used on these fields, which would also be more or less depleted of nutrients in only one year. An adaptation of this would be to burn the same field a second time the year after, because the thicker trees wouldn't burn completely on the first time, and this allowed the harvesting of two crops from the same field. Other variations, particularly in the crops planted, existed as well, but I'm not sure if these were much in use anymore in early modern times; for example, rye, barley and turnips could be planted in the same field, so that first the barley would be harvested in late summer, then the turnips in the fall, and the rye the next year.
Regarding the timelines, I didn't notice any good info on how much each method was used and when, but even the third, newest method mentioned above was definitely known prior to the resettling of Finns from central and eastern Finland to central Sweden in the 16th century, and thus it was also known to the Finnish settlers in New Sweden. Also, as a sidenote, potatoes didn't become common in Finland until the 1700s, so even though they probably were also planted in slash-and-burn fields then, they're not relevant to this question.
I wasn't able to find quite as many details on Lenape farming techniques other than that they used slash-and-burn agriculture to grow the common North American "Three Sisters" combination of corn/maize, winter squash, and beans. While to some extent this may be similar due to planting several crops in the same field, at least to my modern eyes there are more differences due to the heavier emphasis on squash & beans instead root vegetables and grains. Simultaneous planting of multiple crop plants in the same field isn't a technique shared only by Finnish & Lenape traditions, either, it's actually common across most cultures that practice slash-and-burn agriculture.
Which brings me to my conclusion: Based on this admittedly fairly cursory and casual research, I wouldn't say the similarities are that striking. Sure, there are similarities, but many are already explained by the fact that they're simply good practices in slash-and-burn in general and thus have been "invented" many times over all across the world and throughout history. Some more similarities stem from somewhat similar climate and forest types (at least when compared to tropical jungles and the like).
It's unfortunate that Bailyn doesn't clarify at all what he meant by that one-line comment, which leads me to think that perhaps it was just intended to draw similarities between the early Finnish settlers to show that they had more in common than the Lenape had with e.g. English or Dutch settlers. The earliest Finnish settlers came to New Sweden along the Delaware River starting in the 1640s, where the Swedes tended to stick closer to more "civilized" or urban areas, but the Finns were fine with settling in the wilder forests and were in closer contact with the local natives. The Swedes were in conflict with the English colony of Maryland, where New Sweden apparently leveraged their better relations with the native peoples to gain them as allies, and New Sweden was later conquered by the Dutch. I've heard/read of this narrative of Finnish settlers getting along better with natives due to similar cultural practices, e.g. log cabins (there are claims these were introduced to North America by Finnish settlers), slash-and-burn agriculture, "respecting the land/nature", hunting more sustainably, etc. before, both for the New Sweden colony in the Delaware river area, but also sometimes for later settlers in the 1800s.